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Magazine Problem 54
For Exercises \(51-54,\) solve for the angle \(\theta,\) where \(0 \leq \theta \leq 2 \pi\). $$\cos 2 \theta+\cos \theta=0$$
Problem 55
The tangent sum formula The standard formula for the tangent of the sum of two angles is $$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}$$ Derive the formula.
Problem 55
In Exercises \(47-58,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ h(t)=\frac{1}{t-1} $$
Problem 56
In Exercises \(47-58,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ h(t)=\left|t^{3}\right| $$
Problem 57
Exercises \(57-66\) tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph. $$ y=x^{2}-1, \quad \text { stretched vertically by a factor of } 3 $$
Problem 57
In Exercises \(47-58,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ h(t)=2 t+1 $$
Problem 58
Exercises \(57-66\) tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph. $$ y=x^{2}-1, \quad \text { compressed horizontally by a factor of } 2 $$
Problem 58
In Exercises \(47-58,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ h(t)=2|t|+1 $$
Problem 59
Exercises \(57-66\) tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph. $$ y=1+\frac{1}{x^{2}}, \quad \text { compressed vertically by a factor of } 2 $$
Problem 59
A triangle has sides \(a=2\) and \(b=3\) and angle \(C=60^{\circ} .\) Find the length of side \(c .\)
