91Ó°ÊÓ

Evaluating Trigonometric Functions, find each value of \(\theta\) in degrees \(\left(0^{\circ}<\theta<90^{\circ}\right)\) and radians \((0<\theta<\pi 2)\) without using a calculator. $${ (a) }\csc \theta=\frac{2 \sqrt{3}}{3} \quad \text { (b) } \sin \theta=\frac{\sqrt{2}}{2}$$

Describing a Transformation, g is related to a parent function \(f(x)=\sin (x)\) or \(f(x)=\cos (x)\) . (a) Describe the sequence of transformations from \(f\) to \(g\) . (b) Sketch the graph of \(g\) . (c) Use function notation to write \(g\) in terms of \(f .\) $$ g(x)=\sin (4 x-\pi) $$

Find the exact value of the expression. (Hint: Sketch a right triangle.) \(\sin \left[\arccos \left(-\frac{2}{3}\right)\right]\)

Think About It Because \(f(t)=\sin t\) is an odd function and \(g(t)=\cos t\) is an even function, what can be said about the function \(h(t)=f(t) g(t) ?\)

Using a Reference Angle. Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$\frac{5 \pi}{4}$$

Find the exact value of the expression. (Hint: Sketch a right triangle.) \(\cot \left(\arctan \frac{5}{8}\right)\)

The bearing \(\mathrm{N} 24^{\circ} \mathrm{E}\) means 24 degrees north of east.

Evaluating Trigonometric Functions, find each value of \(\theta\) in degrees \(\left(0^{\circ}<\theta<90^{\circ}\right)\) and radians \((0<\theta<\pi 2)\) without using a calculator. $${ (a) }\cot \theta=\frac{\sqrt{3}}{3} \quad \text { (b) } \sec \theta=\sqrt{2}$$

Describing a Transformation, g is related to a parent function \(f(x)=\sin (x)\) or \(f(x)=\cos (x)\) . (a) Describe the sequence of transformations from \(f\) to \(g\) . (b) Sketch the graph of \(g\) . (c) Use function notation to write \(g\) in terms of \(f .\) $$ g(x)=\sin (2 x+\pi) $$

Using a Reference Angle. Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$\frac{7 \pi}{6}$$