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sin(30) = sin(90 - 60) = sin(90)*cos(60) - cos(90)*sin(60)
= 1*cos(60) - 0*sin(60) = cos(60).
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What is the cosine of a 60 degree angle?
Cosine is 0.5
Is the cosine function an odd function?
No. Cosine, along with sec, is an even function. The odd functions are sin, tan, csc, and cot. The reason for this is because is you take the opposite of the y-value for the cosine function, the overall value of the function is not affected.Take, for example, cos(60 degrees), which equals POSITIVE 1/2.If you flip it over the x-axis, making the y's negative, it becomes cos(-60 degrees), or cos(300 degrees). This equals POSITIVE 1/2.Now let's look at an odd function. For example, sin(30 degrees) equals POSITIVE 1/2. Now take the opposite of this.sin(-30 degrees), or sin(330 degrees), equals NEGATIVE 1/2. This is because it is found in the fourth quadrant, where the y's are negative. Sine of theta, by definition, is y divided by r. If y is negative, sine is negative.
What is the sine of 57degrees 12 minutes?
In angle measurement, 60 minutes = 1° 57° 12' = 57.2 ° Sin 57.2 = 0.84057 (5dp)
What is sin cos tan csc sec cot of 30 45 60 degrees?
Sin(30) = 1/2 Sin(45) = root(2)/2 Sin(60) = root(3)/2 Cos(30) = root(3)/2 Cos(45) = root(2)/2 Cos(60) = 1/2 Tan(30) = root(3)/3 Tan(45) = 1 Tan(60) = root(3) Csc(30) = 2 Csc(45) = root(2) Csc(60) = 2root(3)/3 Sec(30) = 2root(3)/3 Sec(45) = root(2) Sec(60) = 2 Cot(30) = root(3) Cot(45) = 1 Cot(60) = root(3)/3
What is a quadrantal angle?
A Quadrantal angle is an angle that is not in Quadrant I. Consider angle 120. You want to find cos(120) . 120 lies in quadrant II. Also, 120=180-60. So, it is enough to find cos(60) and put the proper sign. cos(60)=1/2. Cosine is negative in quadrant II, Therefore, cos(120) = -1/2.
Why is cosine 60 sine 30?
If you look at the graphs of y=sin(x) and y=cos(x) you can see that the two sinusoidal curves are actually the same graph, but that one is just a shifted version of the other. This type of shift may be referred to as a phase shift. This shift allows certain values of sine and cosine to be equivalent, but to occur at different angle values. You may wish to experiment with other values to better understand the relationship between the two. Such as at 45 degrees: at this value cosine and sine are equal.
What is cosine of 60?
The cosine of 60 degrees is 0.5
The length of the hypotenuse of a 30-60 right triangle is 12 inches find the length of the side opposite the 30 angle?
Use the sine ratio: sine 30 = opposite/12 opposite = 12*sine 30 opposite = 6 inches
If an angle decreases from 60 degrees to 30 degrees the trigonometric function that decreases is the sine?
Yes, the sine decreases, and so does the tangent.
What is the cosine of a 60 degree angle?
Cosine is 0.5
How do you find length of a hypotenuse of a 30 60 90 degree triangle is 7 cm what is the perimeter?
The length of the other two sides is 7 cosine (60) and 7 cosine (30)that is 3.5 and 6.062 cmthe perimeter = 7 + 3.5 + 6.062 = 16.562 cm
The hypotenuse of a 30 - 60 - 90 triangle measures 2 feet How long is the short leg of this triangle?
Use the sine ratio: sine 30 degrees = opposite/hypotenuse Then: opposite = 2*sine 30 degrees Answer: 1 foot
The hypotenuse of a 30-60-90 triangle has length 19 What is the length of the side opposite the 60 angle?
If the hypotenuse of a 30-60-90 triangle has a length of 19, the length of the side opposite the 60 degree angle is: 16.45. (the other leg would be 9.5)sine 60 degrees = opposite/hypotenuseOpposite = 19*sine 60 degreesOpposite = 16.45448267 or 16.45 units to two decimal places
How to figure the length of one side of a triangle with only the length of the long side and some degrees?
you might be able to use tangent, sine, or cosine. you might be able to use the Pythagorean theorem, or you can used 30-60-90 triangle theorem or 45-45-90 triangle theorem
Is the cosine function an odd function?
No. Cosine, along with sec, is an even function. The odd functions are sin, tan, csc, and cot. The reason for this is because is you take the opposite of the y-value for the cosine function, the overall value of the function is not affected.Take, for example, cos(60 degrees), which equals POSITIVE 1/2.If you flip it over the x-axis, making the y's negative, it becomes cos(-60 degrees), or cos(300 degrees). This equals POSITIVE 1/2.Now let's look at an odd function. For example, sin(30 degrees) equals POSITIVE 1/2. Now take the opposite of this.sin(-30 degrees), or sin(330 degrees), equals NEGATIVE 1/2. This is because it is found in the fourth quadrant, where the y's are negative. Sine of theta, by definition, is y divided by r. If y is negative, sine is negative.
How do you find Sins and Cosines without and calculator For example sin 120?
Assuming you don't want the answer of "instead of an electronic calculator you can look it up in a table in a book, use a slide rule, use a computer"... The Sine and Cosine of all acute angles are positive and are the ratios between two of the sides of a right angled triangle where the three sides are: Hypotenuse - side opposite the right (90°) angle; Adjacent - the side next to the angle which is not the hypotenuse; Opposite - the side opposite the angle (the third side of the triangle); then: sine = opposite/hypotenuse cosine = adjacent/hypotenuse For obtuse angles: sine angle = sine (180° - angle) cosine angle = - cosine (180° - angle) For reflex angles180° to 270°: sine angle = -sine (angle - 180°) cosine angle = - cosine (angle - 180°) For reflex angles270° to 360°: sine angle = -sine (360° - angle) cosine angle = cosine (360° - angle) For some angles, an exact value can be found. 30° and 60°: By dropping a perpendicular of an equilateral triangle a triangle with angles 30°, 60° and 90° is formed, If the original triangle had sides of 2 units, the right angled triangle has sides 1, 2 and √3 (as found by Pythagoras), thus: sin 30° = cos 60° = 1/2 sin 60° = cos 30° = √3 / 2 45°: For an isosceles triangle with a right angle between the equal sides, the side lengths are 1, 1 and √2, and the equal angles are 45° giving: sin 45° = cos 45° = 1/√2 The actual values for sine and cosine can be calculated from the sum of two infinite series as long as the angle x is measured in radians; to convert degrees to radians: angle_in_radians = angle° x π / 180° However, for practical purposes only the first few terms of each series need be used as further terms would not affect the value to the required accuracy: sin (x) = x - x³/3! + x^5/5! - x^7/7! + ... = Σ (-1)^r x^(2r+1)/(2r+1)! for r = 0,1, 2, ... cos(x) = 1 - x²/2! + x^4/4! - x^6/6! + ... = Σ (-1)^r x^(2r)/(2r)! for r = 0,1, 2, ... where n! means factorial n, ie n x (n-1) x (n-2) x ... x 2 x 1. eg 3! = 3 x 2 x 1 = 6 eg 5! = 5 x 4 x 3 x 2 x 1 = 120
Why is cosine used in finding ditance traveed on a latitude?
The distance along one degree of longitude is 60 nautical miles at the equator and less at latitudes away from the equator. In fact it is 60 nautical miles times the cosine of the latitude, so 60 at the equator zero at the poles, and 30 nautical miles at 60 degrees north or south..
