91Ó°ÊÓ

Find the complete solution in radians of each equation. $$ 2 \sin \theta+1=\csc \theta $$

Geometry The lengths of the adjacent sides of a parallelogram are 21 \(\mathrm{cm}\) and 14 \(\mathrm{cm} .\) The smaller angle measures \(58^{\circ} .\) What is the length of the shorter diagonal? Round your answer to the nearest centimeter.

Simplify each expression. $$ \frac{\cos 2 \theta}{\sin \theta+\cos \theta} $$

Verify each identity. $$ \frac{\sec \theta}{\cot \theta+\tan \theta}=\sin \theta $$

Open-Ended Choose an angle measure \(A .\) a. Find \(\sin A\) and \(\cos A .\) b. Use an identity to find \(\sin 2 A\) c. Use an identity to find \(\cos \frac{A}{2}\)

Critical thinking Does the Law of Cosines apply to a right triangle? That is does \(c^{2}=a^{2}+b^{2}-2 a b \cos C\) remain true when \(\angle C\) is a right angle? Justify your answer.

Use the definitions of trigonometric ratios in right \(\triangle A B C\) to verify each identity. \(\sec A=\frac{1}{\cos A}\)

Rewrite each expression as a trigonometric function of a single angle measure. $$ \frac{\tan 3 \theta-\tan \theta}{1+\tan 3 \theta \tan \theta} $$

Two sides of a scalene triangle are 9 \(\mathrm{m}\) and 14 \(\mathrm{m}\) . The area of the triangle is 31.5 \(\mathrm{m}^{2} .\) Find the measure of one of the angles of the triangle to the nearest tenth of a degree. Show your work.

Find the complete solution in radians of each equation. $$ 3 \tan ^{2} \theta-1=\sec ^{2} \theta $$