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.

$\(\cos\)105\(\degree\)$

Find the exact value of the expression.

$\(\sin\)15\(\degree\)$

Find the exact value of the expression.

$\(\cos\]\frac{5\pi}{12}\)$

Find the exact value of the expression.

$\(\cos\)80\(\degree\[\cos\)20\(\degree\)+\(\sin\)80\(\degree\]\sin\)20\(\degree\)$

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

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

Find the exact value of the expression.

$\(\tan\)105\(\degree\)$

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=\(\frac\)12$, $\(\sin\) b=\(\frac\)12$, & $a$ is in Q IV and $b$ is in Q II.