6.03 Symmetries
Let \theta be an acute angle in radians. If \sin \theta = 0.6, find the value of the following:
\sin \left(180 - \theta\right)
\sin \left(180 + \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(180 - \theta\right)
\cos \left(180 + \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(180 - \theta\right)
\tan \left(180 + \theta\right)
\tan \left( 360 - \theta\right)
\tan \left( - \theta \right)
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 - 90\right).
Find the value of \sin \left(s - 90\right).
Find the value of \cos \left(s - 90\right).
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(90 - x\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 + 60\right) = \cos \left( 4 x + 20\right)
Simplify:
\dfrac{\cos \left(90 - x\right)}{\cos \left(x\right)}
\sin \left(90 \degree - y\right) \times \tan y