Let \theta be an acute angle in radians. If \sin \theta = 0.6, find the value of the following:
\sin \left(\pi - \theta\right)
\sin \left(\pi + \theta\right)
\sin \left( 2 \pi - \theta\right)
\sin \left( - \theta \right)
Let \theta be an acute angle in radians. If \cos \theta = 0.1, find the value of the following:
\cos \left(\pi - \theta\right)
\cos \left(\pi + \theta\right)
\cos \left( 2 \pi - \theta\right)
\cos \left( - \theta \right)
Let \theta be an acute angle in radians. If \tan \theta = 0.52, find the value of the following:
\tan \left(\pi - \theta\right)
\tan \left(\pi + \theta\right)
\tan \left( 2 \pi - \theta\right)
\tan \left( - \theta \right)
If \sin \dfrac{2 \pi}{11} = 0.5406, find the value of \sin \dfrac{9 \pi}{11} correct to four decimal places.
If \cos \dfrac{2 \pi}{9} = 0.7660, find the value of \cos \dfrac{7 \pi}{9} correct to four decimal places.
If \tan \dfrac{3 \pi}{7} = 4.3813, find the value of \tan \dfrac{4 \pi}{7} correct to four decimal places.
Suppose s is a real number that corresponds to the point \left( - \dfrac{8}{17} , \dfrac{15}{17}\right) on the unit circle:
Find the coordinates of \left(s - \dfrac{\pi}{2}\right).
Find the value of \sin \left(s - \dfrac{\pi}{2}\right).
Find the value of \cos \left(s - \dfrac{\pi}{2}\right).
Suppose s is a real number that corresponds to the point \left( - \dfrac{3}{13} , \dfrac{4\sqrt{10}}{13}\right) on the unit circle:
Find the coordinates of \left(s + \dfrac{\pi}{2}\right).
Find the value of \sin \left(s + \dfrac{\pi}{2}\right).
Find the value of \cos \left(s + \dfrac{\pi}{2}\right).
For each of the following acute angles, state the complementary angle:
Consider the following right triangle:
Find an expression for the following:
\cos \theta
\sin \left(90 \degree - \theta\right)
\sin \theta
\cos \left(90 \degree - \theta\right)
Describe the rule found in part (a) using words.
If \sin \alpha = 0.32, find \cos\left(90\degree-\alpha\right).
If \sin \alpha = \cos \beta, find \alpha + \beta.
Find the acute angle \theta in the following equations:
Given that \sin x = 0.19, find the exact value of \cos \left(\dfrac{\pi}{2} - x\right).
Find the exact value of c, if \sin \left(\dfrac{\pi}{9} + c\right) = \cos \left(\dfrac{\pi}{4}\right).
Find the value of x in the following equations:
\sin \left( 5 x + 40 \degree\right) = \cos \left( 3 x + 10 \degree\right)
\sin \left( 6 x + \dfrac{\pi}{3}\right) = \cos \left( 4 x + \dfrac{\pi}{9}\right)
Simplify:
\dfrac{\cos \left(\dfrac{\pi}{2} - x\right)}{\cos \left(x\right)}
\sin \left(90 \degree - y\right) \times \tan y
Prove that \dfrac{\sin x \cos \left(\dfrac{\pi}{2} - x\right)}{\cos x \sin \left(\dfrac{\pi}{2} - x\right)} = \tan ^{2}\left(x\right).
State the exact value of the following:
\sin ^{2}\left(20 \degree\right) + \cos ^{2}\left(20 \degree\right)
\sin ^{2}\left(\dfrac{\pi}{5}\right) + \cos ^{2}\left(\dfrac{\pi}{5}\right)
Given that \cos x = \dfrac{12}{13} where x is in the first quadrant:
Find the exact value of \sin x.
Find the exact value of \tan x.
Prove the following:
\sin ^{2}x = 1- \cos ^{2}x
Given that \sin \theta = \dfrac{\sqrt{3}}{2}, where 90 \degree < \theta < 180 \degree:
In which quadrant does angle \theta lie?
Find the value of \cos \theta.
Given that \cos y = - \dfrac{5}{13}, where 180 \degree < y < 360 \degree:
In which quadrant does angle y lie?
Find the value of \tan y.
Simplify the following expressions:
\tan \theta \cos \theta
\left(\cos \theta - \sin \theta\right)^{2}
\dfrac{1 - \cos ^{2}\left(\theta\right)}{1 - \sin ^{2}\left(\theta\right)}
\dfrac{1}{1 - \cos \theta} + \dfrac{1}{1 + \cos \theta}
Prove the following identities:
\dfrac{\sin x}{\cos x \tan x} = 1
\dfrac{\sin x \cos x}{\tan x} = \cos ^{2}\left(x\right)
\dfrac{\sin ^{2}\left(x\right) + \sin x \cos x}{\cos ^{2}\left(x\right) + \sin x \cos x} = \tan x
\dfrac{\sin \theta}{1 - \cos \theta} = \dfrac{1 + \cos \theta}{\sin \theta}