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Find the missing measures. Write all answers in radical form.

Find the missing measures. Write all answers in radical form. 30 °. 45 °. x. 7. 10. z. 45 °. w. 60 °. y. The Trigonometric Functions we will be looking at. SINE. COSINE. TANGENT. The Trigonometric Functions. SIN E. COS INE. TAN GENT. SIN E. Prounounced “sign”. COS INE.

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Find the missing measures. Write all answers in radical form.

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  1. Find the missing measures. Write all answers in radical form. 30° 45° x 7 10 z 45° w 60° y

  2. The Trigonometric Functions we will be looking at SINE COSINE TANGENT

  3. The Trigonometric Functions SINE COSINE TANGENT

  4. SINE Prounounced “sign”

  5. COSINE Prounounced “co-sign”

  6. TANGENT Prounounced “tan-gent”

  7. Greek Letter q Prounounced “theta” Represents an unknown angle

  8. hypotenuse hypotenuse opposite opposite adjacent adjacent

  9. We need a way to remember all of these ratios…

  10. Some Old Hippie Came A Hoppin’ Through Our Old Hippie Apartment

  11. Sin SOHCAHTOA Opp Hyp Cos Adj Hyp Tan Opp Adj Old Hippie

  12. Finding sin, cos, and tan

  13. SOHCAHTOA 10 8 6

  14. Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 10.8 9 A 6

  15. Find the values of the three trigonometric functions of . ? Pythagorean Theorem: 5 4 (3)² + (4)² = c² 5 = c 3

  16. Find the sine, the cosine, and the tangent of angle A Give a fraction and decimal answer (round to 4 decimal places). B 24.5 8.2 A 23.1

  17. Let’s find the calculator connections. Draw a 30º-60º-90º to help you find sin 30º. Now use your calculator to find sin 30º. So… What is sin 45º? What is cos 27º? What is tan 62º? 1 .8910 1.881

  18. Can using the calculator help us solve this problem? In triangle PQR, mP = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides.

  19. Can using the calculator help us solve this problem? In triangle PQR, mP = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides. Q 16 P R 35

  20. Can using the calculator help us solve this problem? In triangle PQR, mP = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides. Q 16 P R 35

  21. What about indirect measurement? • The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding the kite to the ground, how high is the kite actually flying?

  22. Solution: • The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding the kite to the ground, how high is the kite flying? 100’ h 79º

  23. You try…. A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? tan 71.5° x tan 71.5° 71.5° x = 50 (tan 71.5°) 50 x = 50 (2.98868)

  24. A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? cos 60° x (cos 60°) = 200 200 60° x x X = 400 yards

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