91Ó°ÊÓ

A race car is averaging 180 mph on a circular track with radius \(1 / 4\) mile. Find its angular velocity in radians per minute.

Show that each equation is not an identity. Write your explanation in paragraph form. \(\cos (-y)=-\cos y\)

Find all values of \(\theta\) in the interval \(0^{\circ}, 360^{\circ}\) ) that satisfy each \right. equation. Round approximate answers to the nearest tenth of a degree. $$\cot ^{2} \theta-4 \cot \theta+2=0$$

Find all values of \(\theta\) in the interval \(0^{\circ}, 360^{\circ}\) ) that satisfy each \right. equation. Round approximate answers to the nearest tenth of a degree. $$9 \sin ^{2} \theta+12 \sin \theta+4=0$$

Show that each equation is not an identity. Write your explanation in paragraph form. \(\cos (2 x)=2 \cos x \sin x\)

Verify that each equation is an identity. $$\tan (\pi / 4+x)=\cot (\pi / 4-x)$$

Find all values of \(\theta\) in the interval \(0^{\circ}, 360^{\circ}\) ) that satisfy each \right. equation. Round approximate answers to the nearest tenth of a degree. $$12 \cos ^{2} \theta+\cos \theta-6=0$$

Use identities to simplify each expression. \(1-\frac{1}{\cos ^{2} x}\)

Verify that each equation is an identity. $$\frac{\cos (\alpha+\beta)}{\sin (\alpha-\beta)}=\frac{1-\tan \alpha \tan \beta}{\tan \alpha-\tan \beta}$$

Find all values of \(\theta\) in the interval \(0^{\circ}, 360^{\circ}\) ) that satisfy each \right. equation. Round approximate answers to the nearest tenth of a degree. $$\frac{\tan 3 \theta-\tan \theta}{1+\tan 3 \theta \tan \theta}=\sqrt{3}$$