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target="_blank" rel="nofollow" href="#fb3_img_img_813c5722-db63-5c6b-9c94-881e014839c0.png" alt="math"/>; is in quadrant II

Find:

      437. Given: is in quadrant IV

      Find:

      438. Given: ; is in quadrant III.

      Find:

      439. Given: ;

      Find:

      440. Given: ,

      Find:

Using the Arc Length Formula

      441−445 Solve the problem using the arc length formula , where r is the radius of the circle and is in radians.

      441. The central angle in a circle with a radius of 20 cm is Find the exact length of the intercepted arc.

      442. The central angle in a circle of radius 6 cm is 85°. Find the exact length of the intercepted arc.

      443. Find the radian measure of the central angle that intercepts an arc with a length of inches in a circle with a radius of 13 inches.

      444. The second hand of a clock is 18 inches long. In 25 seconds, it sweeps through an angle of 150°. How far does the tip of the second hand travel in 25 seconds?

      445. How far does the tip of a 15 cm long minute hand on a clock move in 10 minutes?

Evaluating Inverse Functions

       446−450 Find an exact value of y.

      446. ; give y in radians.

      447. ; give y in radians.

      448. ; give y in radians.

      449. ; give y in radians.

450.

Solving Trig Equations for x in Degrees

      451−455 Find all solutions of the equation in the interval . (Recall that the quadrants in standard position are numbered counterclockwise, starting in the upper right-hand corner.)

      451.

      452.

      453.

      454.

      455.

Calculating Trig Equations for x in Radians

      456−460 Find all solutions of the equation in the interval . (Recall that the quadrants in standard position are numbered counterclockwise, starting in the upper right-hand corner.)

      456.

      457.

      458.

      459.

      460.

Chapter 8

      Graphing Trig Functions

      The graphs of trigonometric functions are usually easily recognizable — after you become familiar with the basic graph for each function and the possibilities for transformations of the basic graphs.

      Trig functions are periodic. That is, they repeat the same function values over and over, so their graphs repeat the same curve over and over. The trick is to recognize how often this curve repeats and where one of the basic graphs starts for a particular function.

      An interesting feature of four of the trig functions is that they have asymptotes — those not-really-there lines used as guides to the shape of a curve. The sine and cosine functions don’t have asymptotes, because their domains are all real numbers. The other four functions have vertical asymptotes to mark where their domains have gaps.

The Problems You’ll Work On

      In this chapter, you’ll work with the graphs of trigonometric functions in the following ways:

       Marking any intercepts on the x-axis to help graph the curves

       Locating and drawing in vertical asymptotes for the tangent, cotangent, secant, and cosecant functions

       Computing the change in the period of a function based on some transformation

       Adjusting the amplitude of the sine or cosine when the basic curve has a multiplier

       Making

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