6. Trigonometric Identities and More Equations

Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.

cos(θ - 270°)

Find cos(s + t) and cos(s - t).

cos s = √2/4 and sin t = - √5/6, s and t in quadrant IV

Find one value of θ or x that satisfies each of the following.

cos x = sin (π/12)

Find the exact value of the expression.

$\cos105\degree$

Find the exact value of the expression.

$\sin15\degree$

Find the exact value of the expression.

$\cos\frac{5\pi}{12}$

Find the exact value of the expression.

$\cos80\degree\cos20\degree+\sin80\degree\sin20\degree$

Expand the expression using the sum & difference identities and simplify.

$\sin\left(-\theta-\frac{\pi}{2}\right)$

Find the exact value of the expression.

$\tan105\degree$

Expand the expression using the sum & difference identities and simplify.

$\tan\left(-\theta-\frac{\pi}{2}\right)$

Find $\cos\left(a+b\right)$ given $\cos a=\frac12$, $\sin b=\frac12$, & $a$ is in Q IV and $b$ is in Q II.