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Why do sine and cosine always have values less than 1?
Sine and cosine functions represent the ratios of the lengths of sides of a right triangle relative to the hypotenuse. Since these ratios involve the lengths of the triangle's legs (which are always shorter than or equal to the hypotenuse), the values of sine and cosine cannot exceed 1. Additionally, on the unit circle, the coordinates of any point (x, y) are constrained within the range of -1 to 1, which further reinforces that the maximum and minimum values of sine and cosine are also limited to this range.
What are the values of theta of which secant theta is undefined?
Since secant theta is the same as 1 / cosine theta, the answer is any values for which cosine theta is zero, for example, pi/2.
How does geometric properties help you find the value of trigonometric functions?
Geometric properties, particularly those related to right triangles and the unit circle, provide a visual framework for understanding trigonometric functions. In a right triangle, the ratios of the lengths of the sides (opposite, adjacent, and hypotenuse) directly define sine, cosine, and tangent. Similarly, on the unit circle, the coordinates of points correspond to the values of these functions for different angles, allowing for easy calculation of sine and cosine values. Thus, geometric insights simplify the evaluation and interpretation of trigonometric functions.
What is the Cosine of 62 degrees?
The cosine of 62 degrees is approximately 0.4695. This value can be found using a scientific calculator or trigonometric tables. Cosine values represent the ratio of the adjacent side to the hypotenuse in a right triangle for the given angle.
A tree 40 feet high casts a shadow 58 feet long find the measure of the angle of elevation of the sum?
To find the angle of elevation of the sun, we can use the tangent function. The tangent of an angle is equal to the opposite side (height of the tree) divided by the adjacent side (length of the shadow). So, tan(angle) = height of the tree / length of the shadow. Plugging in the values, we get tan(angle) = 40 / 58. Taking the arctan of both sides gives us the angle, so the angle of elevation of the sun is approximately 33.56 degrees.
How do you use sine cosine and tangent?
They are used to find the angle or side measurement of a right triangle. For example, if 2 sides of a right triangle have known values and an angle has a known measurement, you can find the third side by using sine, cosine or tangent.
What are the domains of sine cosine and tangent?
The domain of a function is the set of values of the independent variable for which the function is valid. In practice, this is the allowable values of X or, in this case, theta. The sine and cosine functions have a domain of all numbers from negative infinity to positive infinity. The tangent function, however, is sine(theta) / cosine(theta). Cosine(theta) has value of zero at theta equal to pi / 2, 3pi/2, 5pi/2, ... in the positive direction, and -pi/2, -3pi/2, -5pi/2, ... As a result, tangent(theta) is undefined at these values, so the domain of tangent is all numbers from negative infinity to positive infinity except all numbers n pi/2 where n is odd.
What can help you remember the ratios for cosine and tangent?
A memory trick that I learned for trigonometric values is:Sin: opp/hypCos: adj/hyptan: opp/adjSoh-Cah-Toa
Which of the six trig functions have values greater than 1?
tangent, cotangent, secant, and cosecant can all be greater than 1 at certain angles
What does the trigonometric table do?
trigonometric table gives the values of all the trigonometric functions for any angle. i.e; it gives the numerical values of sine, cosine, tangent etc for any angle between 0 to 180 degrees the values for other angles can be calculated using these.
Is the cosine sine and tangent of an angle equal to each other?
No; those could be three different values, or sometimes two of them might be the same. For example, if the angle is 45 degrees, the values are about... cos:0.707 sin: 0.707 tan: 1 For 45 degrees, the cosine and sine are the same. For 36 degrees, cos:0.809 sin: 0.588 tan: .727
What is cosine of 3?
Undefined!!!! Can't answer it! All sine and cosine values are between -1 and 1 !!!
How do you find an angle of a right triangle?
you need to have at least 2 values of the lengths of the triangle and then you can find the angle by sine, cosine or tangent formulas you may try this online calculator for right triangles. http://www.rillocenter.com/calculate/trigonometry.html
Why do sine and cosine always have values less than 1?
Sine and cosine functions represent the ratios of the lengths of sides of a right triangle relative to the hypotenuse. Since these ratios involve the lengths of the triangle's legs (which are always shorter than or equal to the hypotenuse), the values of sine and cosine cannot exceed 1. Additionally, on the unit circle, the coordinates of any point (x, y) are constrained within the range of -1 to 1, which further reinforces that the maximum and minimum values of sine and cosine are also limited to this range.
Examples of sohcahtoa?
SOHCAHTOAA way of remembering how to compute the sine, cosine, and tangent of an angle.SOH stands for Sine equals Opposite over Hypotenuse.CAH stands for Cosine equals Adjacent over Hypotenuse.TOA stands for Tangent equals Opposite over Adjacent. Example: Find the values of sin θ,cos θ, and tan θ in the right triangle 3, 4, 5. Answer:sin θ = 3/5 = 0.6cosθ = 4/5 = 0.8tanθ = 3/4 = 0.75
What are the values of theta of which secant theta is undefined?
Since secant theta is the same as 1 / cosine theta, the answer is any values for which cosine theta is zero, for example, pi/2.
What do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
