Trigonometry Expert Q&A

If $\cos \theta=-2/5$ and $\tan\theta>0$, what is $\sin \theta$?

An alternating current generator produces a current given by I= 10 sin (120pi t -pi/2) where t is time in seconds and I is in amperes.

(A) What are the amplitude, frequency, and phase shift for this current?

(B) Explain how you would find the maximum current in this circuit and find it.

(C) Graph the equation in a graphing calculator for $0\leq t \leq 0.1$. How many periods are shown in the graph?

Graph three full periods of each equation.

y = 3 - 2 cos (2x + pi)

(A) Graph both sides of the following equation in the same viewing window for x in [-pi, pi]. Is the equation an identity over the interval x in [-pi, pi]? Explain. (Recall that 3!, read “3 factorial”, is equal to 321 =6 and, similarly, 5! = 120 and 7! = 5040.)

(B) Extend the interval in part (A) to x in [-2pi, 2pi]. Now, does the equation appear to be an identity? What do you observe?

Find the smallest positive number C that makes the statement true.

If the graph of the cosecant function is shifted C units to the left, it coincides with the graph of the secant function.

Write $\sec x$ in terms of $\tan x$.

Write the given expression

$$\sin 7t-\sin 4t$$

as a product of two trigonometric functions of different frequencies.

Find the x- and y-intercepts of the graph of the equation y = 8 - 3x.

Determine whether the expression is a polynomial. If it is, write the polynomial in standard form.

$$2 x^{2}-2 x^{4}-x^{3}+\sqrt{2}$$

Write an equation of the line that passes through the points. Use the slope-intercept form (if possible). If not possible, explain why and use the general form. Use a graphing utility to graph the line (if possible). $(−8, 0.6), (2, −2.4)$

Write each equation in terms of a single trigonometric function. Check the result by entering the original equation in a graphing calculator as $y_1$ and the converted form as $y_2$. Then graph $y_1$ and $y_2$ in the same viewing window. Use TRACE to compare the two graphs.

$$y = \cos 3x \cos x- \sin 3x \sin x$$

Fill in the blanks. A _______ function is a second-degree polynomial function, and its graph is called a _______

Use a graphing calculator to test whether each equation is an identity. If an equation appears to be an identity, verify it. If an equation does not appear to be an identity, find a value of x for which both sides are defined but are not equal.

$$\frac{\sin x}{\cos x\tan (-x)}=-1$$

Write each equation in terms of a single trigonometric function. Check the result by entering the original equation in a graphing calculator as $y_1$ and the converted form as $y_2$. Then graph $y_1$ and $y_2$ in the same viewing window. Use TRACE to compare the two graphs.

$$y = \sin 3x \cos x- \cos 3x \sin x$$

Use sum or difference identities to convert each equation to a form involving sin x, cos x, and/or tan x. To check your result, enter the original equation in a graphing calculator as $y_1$ and the converted form as $y_2$ Then graph $y_1$ and $y_2$ in the same viewing window. Use TRACE to compare the two graphs.

$$y=\tan\left(x + \frac{2\pi}{3}\right)$$