ECON
Trigonometry Lecture Notes_part2

# Example 75 example 76 equations with a multiple angle

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Example 75

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Example 76 Equations with a multiple angle Solve the equation: tan3 1 x = , within the interval:0 2 x π < Example 77 Equations with a multiple angle 3 sin 2 2 x = , 0 2 x π < Example 78 Example 79 2 tan sin 3tan x x x = , within 0 2 x π < Example 80 Using a trigonometric identity to solve a trig equation: cos 2 3sin 2 0 x x + - = , within 0 2 x π < Example 81 Using a trigonometric identity to solve a trig equation: 1 sin cos 2 x x = , within 0 2 x π < Example 82 Using a trigonometric identity to solve a trig equation: sin cos 1 x x - = , within 0 2 x π <
Example 83 Solve the following equation: 7cos 9 2cos θ θ + = - Example 84 Solve the equation on the interval [0,2 π ): Example 85 Solve the equation on the interval [0,2 π ) Example 86 Solve the equation on the interval [0,2 π ) Section 6.7 Applied Problems Solving a right triangle means finding the missing lengths of the sides and the measurements of its angles. We will label the right triangle as is done in the following diagram: Example 87 3 tan 2 3 θ = sin 2 sin x x = 2 cos 2cos 3 0 x x + - =

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Finally, we need to find c. Because we have a known angle, a known adjacent side, and an unknown hypotenuse, we use the cosine function. cos34.5 ° = 10.5/c c=10.5/cos34.5 ° = 12.74 In summary, B = 55.5º, a = 7.22, and c = 12.74. Example 88

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Example 89 A 200 foot cliff drops vertically into the ocean. If the angle of elevation of a ship to the top of the cliff is 22.3 degrees, how far above shore is the ship? Example 90 A building that is 250 feet high cast a shadow that is 40 feet long. Find the angle of elevation of the sun at that time. Example 91 A boat leaves the entrance to a harbor and travels 40 miles on a bearing S 64 ° E. How many miles south and how many miles east from the harbor has the boat traveled?
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