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Trigonometric Ratios for PQR

Find the sine, cosine, and tangent ratios for angle P in triangle PQR, given the lengths of the sides. Use a calculator to find trigonometric ratios for other angles.

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Trigonometric Ratios for PQR

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  1. For PQR, write the sine, cosine, and tangent ratios for P. For P, the length of the opposite side is 5 feet, and the length of the adjacent side is 12 feet. The length of the hypotenuse is 13 feet. EXAMPLE 1 Finding Trigonometric Ratios SOLUTION

  2. = sinP = 5 5 12 = = cosP 13 13 12 = = tanP opposite adjacent opposite adjacent hypotenuse hypotenuse EXAMPLE 1 Finding Trigonometric Ratios

  3. Use a calculator to find sine, cosine, and tangent of 30. sin300.5 = a. 0.8660 cos30 b. 0.5774 c. tan30 EXAMPLE 2 Using a Calculator ANSWER Display Keystrokes

  4. 1. For ABC, write the sine, cosine, and tangent ratios for Aand C. Which ratio has a value greater than 1? 8 8 15 15 17 17 = sinA = = = cosA opposite opposite adjacent hypotenuse adjacent hypotenuse = = tanA for Examples 1 and 2 GUIDED PRACTICE

  5. = cosC = = = tanC 15 8 15 8 17 17 opposite opposite opposite hypotenuse hypotenuse adjacent = sinC = for Examples 1 and 2 GUIDED PRACTICE Tan c has a value greater than to 1

  6. Draw a 45o–45o–90o triangle. Label the legs 2 ft and the hypotenuse appropriately. Write the sine, cosine, and tangent ratios for one of the 45o angles. Does it make a difference which 45o angle you choose? Explain. 2. for Examples 1 and 2 GUIDED PRACTICE ANSWER

  7. = cosA = = = tanA 1 1 1 2 2 1 opposite opposite opposite hypotenuse hypotenuse adjacent = sinA = for Examples 1 and 2 GUIDED PRACTICE It does not make a difference because the opposite and adjacent values are the same.

  8. 3. cos75o ANSWER ANSWER 0.3420 1.1918 4. tan50o for Examples 1 and 2 GUIDED PRACTICE Use a calculator to approximate the expression. Round your answer to four decimal places.

  9. 5. sin25o ANSWER ANSWER 0.4226 0.1228 6. tan 7o for Examples 1 and 2 GUIDED PRACTICE Use a calculator to approximate the expression. Round your answer to four decimal places.

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