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Calculating Sine, Cosine, and Tangent

Calculating Sine, Cosine, and Tangent. *adapted from Walch Education. Key Terms. SINE COSINE TANGENT INVERSE ACUTE ANGLE. SOLVING A TRIANGLE ADJACENT SIDE OPPOSITE SIDE HYPOTENUSE RATIO. Memory, refreshed.

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Calculating Sine, Cosine, and Tangent

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  1. Calculating Sine, Cosine, and Tangent *adapted from Walch Education

  2. Key Terms • SINE • COSINE • TANGENT • INVERSE • ACUTE ANGLE • SOLVING A TRIANGLE • ADJACENT SIDE • OPPOSITE SIDE • HYPOTENUSE • RATIO

  3. Memory, refreshed Notice that the trigonometric ratios contain three unknowns: the angle measure and two side lengths.

  4. What can we do with our trigonometric ratios? • Given an acute angle of a right triangle and the measure of one of its side lengths, we can use sine, cosine, or tangent to find another side. • AND… • WAIT FOR IT…

  5. TADAAAAAAA Given two sides of the right triangle, we can use the inverses of these trigonometric functions (sin–1, cos–1, and tan–1) to find the acute angle measures

  6. HOW? Well, let’s find out! Example : A trucker drives 1,027 feet up a hill that has a constant slope. When the trucker reaches the top of the hill, he has traveled a horizontal distance of 990 feet. At what angle did the trucker drive to reach the top? Round your answer to the nearest degree.

  7. First, let’s sketch it out.

  8. Now I can determine which trig ratio to use… you guessed it, COSINE, since it is the trigonometric function that uses the adjacent side and the hypotenuse

  9. Therefore, Solving for w, = w = w

  10. CALCULATOR TIME! Remember to check that your calculator is in DEGREE, not RADIAN Press (990/1027) , then press enter… and the answer is 15.426 The trucker drove at an angle of 15° to the top of the hill.

  11. Your turn Solving the right triangle means to find all the missing angle measures and all the missing side lengths. Solve the right triangle. Round sides to the nearest thousandth.

  12. GOOD LUCK Thanks for watching ~ Ms. Dambreville

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