Math  /  Trigonometry

QuestionSections 4.7+4.84.7+4.8
Show all work! (1) Find the exact value of each expression. state if undefined. a) arccos(12)\arccos \left(\frac{1}{2}\right) b) arcsin(4)\arcsin (4) c) sin(arcsin(12))\sin \left(\arcsin \left(-\frac{1}{2}\right)\right) d) tan(arccos(37)) sketcl this on the  coordinate plane. \tan \left(\arccos \left(\frac{3}{7}\right)\right) \quad \begin{array}{l}\text { sketcl this on the } \\ \text { coordinate plane. }\end{array} (2) Solve the problem. Use exact values (leave in terms of a trig function. Aski slope is 52 ft long and the angle A ski slope is from the ground to the summit is 4242^{\circ}. How high is the summit? (Draw your best ski slope and mountain) "̈

Studdy Solution
Solve the ski slope problem.
Given: - Hypotenuse (slope) = 5252 ft - Angle = 4242^\circ
We need to find the height of the summit, which is the opposite side of the angle in a right triangle. Use the sine function:
sin(42)=Height52 \sin(42^\circ) = \frac{\text{Height}}{52}
Solve for Height:
Height=52sin(42) \text{Height} = 52 \cdot \sin(42^\circ)
Since we need the exact value in terms of a trig function:
Height=52sin(42) \text{Height} = 52 \cdot \sin(42^\circ)
The solutions are: a) π3\frac{\pi}{3} b) Undefined c) 12-\frac{1}{2} d) 2103\frac{2\sqrt{10}}{3} 2) Height = 52sin(42)52 \cdot \sin(42^\circ)

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