Chapter 1 | Functions and Graphs
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1.18 Evaluate cos(3 π /4) and sin(− π /6).
As mentioned earlier, the ratios of the side lengths of a right triangle can be expressed in terms of the trigonometric functions evaluated at either of the acute angles of the triangle. Let θ be one of the acute angles. Let A be the length of the adjacent leg, O be the length of the opposite leg, and H be the length of the hypotenuse. By inscribing the triangle into a circle of radius H , as shown in Figure 1.33 , we see that A , H , and O satisfy the following relationships with θ : sin θ = O H csc θ = H O cos θ = A H sec θ = H A tan θ = O A cot θ = A O
Figure 1.33 By inscribing a right triangle in a circle, we can express the ratios of the side lengths in terms of the trigonometric functions evaluated at θ .
Example 1.24 Constructing a Wooden Ramp
A wooden ramp is to be built with one end on the ground and the other end at the top of a short staircase. If the top of the staircase is 4 ft from the ground and the angle between the ground and the ramp is to be 10°, how
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