91Ó°ÊÓ

In Problems \(65-70\), using a inverse trigonometric function find the solutions of the given equation in the indicated interval. Round your answers to two decimal places. $$ 20 \cos ^{2} x+\cos x-1=0,[0, \pi] $$

Using a inverse trigonometric function find the solutions of the given equation in the indicated interval. Round your answers to two decimal places. $$ 3 \sin ^{2} x-8 \sin x+4=0,[-\pi / 2, \pi / 2] $$

Show that the given expression is not an identity. $$ (\sin x+\cos x)^{2}=\sin ^{2} x+\cos ^{2} x $$

In Problems \(65-68\), find the measure of a central angle \(\theta\) in a circle of radius \(r\) that subtends an arc length s. Give \(\theta\) in (a) radians and (b) degrees. $$ r=10 \mathrm{in}, s=36 \mathrm{in} $$

Describe in words how you would obtain the graph of the given function by starting with the graph of \(y=\sin x\) (Problem 65 ) and the graph of \(y=\cos x(\) Problem 66\()\). $$ y=-6+\frac{1}{4} \cos \left(\frac{1}{2} x+\pi\right) $$

In Problems \(65-68\), find the measure of a central angle \(\theta\) in a circle of radius \(r\) that subtends an arc length s. Give \(\theta\) in (a) radians and (b) degrees. $$ r=9 \mathrm{~m}, s=15 \mathrm{~m} $$

Rewrite the given function as a single trigonometric function involving no products or squares. Give the amplitude and period of the function. $$ y=4 \cos ^{2} x-2 $$

Using a inverse trigonometric function find the solutions of the given equation in the indicated interval. Round your answers to two decimal places. $$ \tan ^{2} x+\tan x-1=0,(-\pi / 2, \pi / 2) $$

Find the period of the given function. $$ f(x)=\sin \frac{1}{2} x \sin 2 x $$

In Problems \(65-68\), find the measure of a central angle \(\theta\) in a circle of radius \(r\) that subtends an arc length s. Give \(\theta\) in (a) radians and (b) degrees. $$ r=20 \mathrm{~cm}, s=90 \mathrm{~cm} $$