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Warm-UP

Warm-UP. What does SOH CAH TOA stand for? Sin θ = Cos θ = Tan θ = 2. Find the sine cosine and tangent of the acute angles. Round the decimal to four places. Challenge Question! Can the sine, cosine or tangent of a triangle be greater than 1? Why or Why not?

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Warm-UP

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  1. Warm-UP • What does SOH CAH TOA stand for? • Sin θ= Cos θ= Tan θ= • 2. Find the sine cosine and tangent of the acute angles. Round the decimal to four places. • Challenge Question! • Can the sine, cosine or tangent of • a triangle be greater than 1? • Why or Why not? • The sine and the cosine cannot because this would mean the opposite or adjacent side is greater than the hypotenuse. The tangent can because one leg can be bigger than another leg.

  2. More Trigonometry

  3. Learning Outcomes • I will be able to use trigonometric ratios to find missing side lengths of a right triangle • I will be able to use trigonometric ratios to find missing angle measures of a right triangle

  4. Using Trigonometry Ratios 28° • In your homework you will be given a problems like this. • Is there enough information to use the Pythagorean theorem to solve this problem? y 13 x

  5. Using Trigonometric Ratios 28° • Since there’s not enough information to solve this with the Pythagorean Theorem. How might our trig. ratios help us? • sin θ= • cosθ= • tan θ = y 13 x

  6. Using Trigonometric Ratios 28° • Let’s solve this problem. • Step 1.) Label the triangle • Step 2.) Fill In your trig ratios • sin 28° = cos 28°= tan 28° = • Notice that the tangent has two unknowns. In this example the tangent does not help us. Adj. y 13 Hyp. x Opp.

  7. Using Trigonometric Ratios 28° • Now solve for x • sin28° = • x =13· sin 28 ≈ 6.1031 • cos28° = • y = 13·cos28 ≈ 11.4783 (13) (13) y 13 (13) (13) x Do our answers make sense?

  8. Using Trigonometric Ratios 28° • Let’s solve this problem. • Step 1.) Label the triangle • Step 2.) Fill In your trig ratios • sin 28° = cos 28°= tan 28° = • Notice that the cosine has two unknowns. In this example the cosine does not help us. Adj. y x Hyp. 13 Opp.

  9. Using Trigonometric Ratios 28° • Now solve for x • sin28° = • x · sin 28° = 13 • x =≈ 27.6907 • tan 28° = • y· tan28° = 13 • y =≈ 24.4494 (x) (x) y x (y) (y) 13 Do our answers make sense?

  10. Let’s Practice! SOH CAH TOA • Solve for x. hyp. opp. adj. x ≈ 11.8202 x ≈ 11.1809 x ≈ 17.9683

  11. A How can I find Angles using Trig? 5 • How can I use trig to find the measure of angle A and angle C? • Let’s set up a trig ratios for A using sine. • sinA= • Now to solve for A we have to use the inverse of sin. 3 B C 4 sin‾¹ (sin A) =sin‾¹() A = sin‾¹() A ≈ 53.1301 ° Solve for A using the other two trig functions. Do you get the same answer?

  12. A How can I find Angles using Trig? 5 • How can I use trig to find the measure of angle A and angle C? • Try to find the angle measure for C. • sin C = • cosC = • tanC = 3 C = sin‾¹() C≈ 36.8699° B C 4 C = cos‾¹() C ≈ 36.8699° C = tan‾¹() C ≈ 36.8699°

  13. Let’s Practice! • Find the missing angles and side of the right triangle. m∠A≈ 48.2 m∠B≈ 41.8 BC = 4√5 m∠R≈ 54.0 m∠T≈ 36.0 RT = √185

  14. Exit Ticket Homework • Pg. 563: 28-36, 39,40 and Pg. 570: 14-33 • Solve for x and y.

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