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Warm up

Warm up. State the domain for : If f(x) = x 3 – 2x +5 find f(-2). Right Triangle Trigonometry. Objective To learn the trigonometric functions and how they apply to a right triangle. The Trigonometric Functions we will be looking at. SINE. COSINE. TANGENT. The Trigonometric Functions.

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Warm up

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  1. Warm up • State the domain for: • If f(x) = x3 – 2x +5 find f(-2)

  2. Right Triangle Trigonometry Objective To learn the trigonometric functions and how they apply to a right triangle.

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

  4. The Trigonometric Functions SINE COSINE TANGENT

  5. SINE Prounounced “sign”

  6. COSINE Prounounced “co-sign”

  7. TANGENT Prounounced “tan-gent”

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

  9. hypotenuse hypotenuse opposite opposite adjacent adjacent

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

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

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

  13. Finding sin, cos, and tan

  14. SOHCAHTOA 10 8 6

  15. 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

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

  17. Sine • Find the sin of α β 8 α A 10 C

  18. 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

  19. Cosine • Find the cosine and tan of α β 6 5 α A √11 C

  20. Relationship between Sine and Cosine • Sin (α) = cos ( ) β 5 3 α A 4 C

  21. Relationship between Sine and Cosine • Look at the Pythagorean Theorem • (adj)2 + (opp)2 = (hyp)2 • Divide each side by (hyp)2 • (adj)2+ (opp)2= (hyp)2 • (hyp)2 (hyp)2 (hyp)2

  22. Relationship between Sine and Cosine • (adj)2+ (opp)2= 1 • (hyp)2 (hyp)2 • (sin (x))2 + (cos (x))2 = 1 • sin2(x) + cos2(x) = 1

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