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How do you simplify bracket 1 plus tan theta bracket bracket 5 sin theta -2 bracket equals 0?
(in a past paper it asks u to solve this for -180</=theta<180, so I have solved it) Tan theta =-1, so theta = -45. Use CAST diagram to find other values of theta for -180</=theta<180: Theta (in terms of tan) = -ve, other value is in either S or C. But because of boundaries value can only be in S. So other value= 180-45=135. Do the same for sin. Sin theta=2/5 so theta=23.6 CAST diagram, other value in S because theta (in terms of sin)=+ve. So other value=180-23.6=156.4.
What is the exact value of sin 165?
The exact value of (\sin 165^\circ) can be calculated using the sine subtraction formula. Since (165^\circ = 180^\circ - 15^\circ), we have: [ \sin 165^\circ = \sin(180^\circ - 15^\circ) = \sin 15^\circ ] The value of (\sin 15^\circ) can be derived from the formula (\sin(45^\circ - 30^\circ)), which gives: [ \sin 15^\circ = \sin 45^\circ \cos 30^\circ - \cos 45^\circ \sin 30^\circ = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} - \sqrt{2}}{4} ] Thus, (\sin 165^\circ = \frac{\sqrt{6} - \sqrt{2}}{4}).
Find the value of tan 180 plus 15?
For tan(180 degrees), this is simply sin(180 degrees)/cos(180 degrees). To find these values, note that 180 degrees is the leftmost point on the unit circle, at y=0, x=-1, so is tan(180 degrees)=0/-1=0. Then adding 15 gives 15.
What are the values of theta of which co secant theta is undefined?
Any value for which sin(theta) = 0, i.e. theta = N*180, N being an Integer.
Determine the measure of angle A if 0 degrees is smaller than or equal to A which is smaller than or equal to 90 degrees and cos125 degrees equals negative cos A?
cos(125) = cos(180 - 55) = cos(180)*cos(55) + sin(180)*sin(55) = -cos(55) since cos(180) = -1, and sin(180) = 0 So A = 55 degrees.
What is the sin 180?
The sine of 180 degrees is 0. This is because, on the unit circle, the point corresponding to 180 degrees is located at (-1, 0), and the sine value represents the y-coordinate of that point. Therefore, sin(180°) = 0.
Verify cot x-180 cot x?
cot x = (cos x) / (sin x) cos (x - 180) = cos x cos 180 + sin x sin 180 = - cos x sin (x - 180) = sin x cos 180 - cos x sin 180 = - sin x cot (x - 180) = (cos (x - 180)) / (sin (x - 180)) = (- cos x) / (- sin x) = (cos x) / (sin x) = cot x
How do you find value of sine when angle greater than 90?
For angles greater than 360 degrees, subtract multiples of 360 so that the relevant angle (the remainder) is between 0 and 360 degrees. Then For 90 < x ≤ 180 deg, sin(x) = sin(180-x) For 180 < x ≤ 270 deg, sin(x) = -sin(x-180) For 270 < x ≤ 360 deg, sin(x) = -sin(360-x)
How do you simplify bracket 1 plus tan theta bracket bracket 5 sin theta -2 bracket equals 0?
(in a past paper it asks u to solve this for -180</=theta<180, so I have solved it) Tan theta =-1, so theta = -45. Use CAST diagram to find other values of theta for -180</=theta<180: Theta (in terms of tan) = -ve, other value is in either S or C. But because of boundaries value can only be in S. So other value= 180-45=135. Do the same for sin. Sin theta=2/5 so theta=23.6 CAST diagram, other value in S because theta (in terms of sin)=+ve. So other value=180-23.6=156.4.
What is the sine of 180?
The sine of 180 degrees is 0. Remember, the sine value on a unit circle is the y-value. If you find f(pi) in the function f(x)=sin(x), you will get zero as an answer.
What is sin of -pi?
sin(-pi) = sin(-180) = 0 So the answer is 0
What is the exact value of sin 165?
The exact value of (\sin 165^\circ) can be calculated using the sine subtraction formula. Since (165^\circ = 180^\circ - 15^\circ), we have: [ \sin 165^\circ = \sin(180^\circ - 15^\circ) = \sin 15^\circ ] The value of (\sin 15^\circ) can be derived from the formula (\sin(45^\circ - 30^\circ)), which gives: [ \sin 15^\circ = \sin 45^\circ \cos 30^\circ - \cos 45^\circ \sin 30^\circ = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} - \sqrt{2}}{4} ] Thus, (\sin 165^\circ = \frac{\sqrt{6} - \sqrt{2}}{4}).
What is the value of sin(1pi)?
The value of sin(1) is 0.
How do you calculate trigonometric ratios of obtuse angles?
If ø is an obtuse angle then (180 - ø) is an acute angle and: sin ø = sin (180 - ø) cos ø = -cos (180 - ø) tan ø = -tan (180 - ø)
Find the value of tan 180 plus 15?
For tan(180 degrees), this is simply sin(180 degrees)/cos(180 degrees). To find these values, note that 180 degrees is the leftmost point on the unit circle, at y=0, x=-1, so is tan(180 degrees)=0/-1=0. Then adding 15 gives 15.
What are the values of theta of which co secant theta is undefined?
Any value for which sin(theta) = 0, i.e. theta = N*180, N being an Integer.
Determine the measure of angle A if 0 degrees is smaller than or equal to A which is smaller than or equal to 90 degrees and cos125 degrees equals negative cos A?
cos(125) = cos(180 - 55) = cos(180)*cos(55) + sin(180)*sin(55) = -cos(55) since cos(180) = -1, and sin(180) = 0 So A = 55 degrees.
