9514 1404 393
Answer:
- θ = 56°
- θ = 65°
- θ = 45°
Step-by-step explanation:
In general, you solve equations like these by getting the function of the variable by itself on one side of the equal sign. Then you use the inverse function to find the argument of the function. As in problem 3, you may have to go another step or two to get from the value of the function argument to the value of the variable.
1. We need to find sin(θ), then use the arcsine function.
sin(θ) -0.832 = 0 . . . . given
sin(θ) = 0.832 . . . . . . add 0.832 to both sides
θ = arcsin(0.832) ≈ 56.305° . . . . . . use the inverse sine function to find θ
θ ≈ 56°
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2. 1/2cos(θ) = 0.214 . . . . given
cos(θ) = 0.428 . . . . . . multiply by 2
θ = arccos(0.428) ≈ 64.659° . . . . use the inverse cosine function
θ ≈ 65°
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3. 3tan(θ -20°) = 1.43 . . . . given
tan(θ -20°) = 0.47666... . . . divide by 3
θ -20° = arctan(0.47666...) . . . . use the arctan function to find θ-20°
θ -20° ≈ 25.486°
θ = 45.486° . . . . . . . add 20°
θ ≈ 45°
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<em>Additional comments</em>
Scientific and graphing calculators often require use of a <em>2nd</em> or <em>SHIFT</em> key to access the inverse trig functions. The inverse function often uses the same key on the calculator. These are generally marked with a -1 superscript: a key might be marked with sin, for example, with sin⁻¹ as its alternate function.
The trig functions of a calculator will usually deal with angles in any of several units. The most common of these are degrees, grads, and radians. Usually, you are required to set the calculator mode to make use of one or the other of these angle measures. For this problem, you need to be sure the calculator is set to <em>degrees mode</em>.
