6.02 Trigonometric identities
State the exact value of the following:
\sin ^{2}\left(20 \degree\right) + \cos ^{2}\left(20 \degree\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.
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}
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.