Foundations to college algebra Trigonometry Right Triangle Trig

1. Foundations to college algebra TrigonometryRight Triangle Trig Lesson 1 Objective:I will learn the definition of trigonometry, learn the ratios of , cosine and .

2. Definitions is the study of relationships among the angles and sides of a right triangle. Trigonometric is the fraction that compares the of a right triangle. Trigonometric is the specific rule (combination of sides) given by the ratio. There are a total of 6 trig functions: sine, cosine, tangent, cosecant, secant and cotangent.

3. Each Trig function has a unique ratio of . Today we will focus on the three on the left. sin θ = opp csc θ = hyp hyp opp cos θ = adj sec θ = hyp hyp adj tan θ = opp cot θ = adj adj opp An easy acronym this side is ALWAYS for this side is: the reciprocal of the function on the left

4. Write the trig ratios of sin, cos and tan for each of the acute angle of the right triangle. Include the formula for each function and simplify all radicals. No decimals 6 8 sin B = cos B = tan B = B A 10 sin A = cos A = tan A =

5. Write the trig ratios of sin, cos and tan for each of the acute angle of the right triangle. Include the formula for each function and simplify all radicals. No decimals sin B = cos B = tan B = sin A = cos A = tan A = A 3 3 6 B 3

6. Write the trig ratios of sin, cos and tan for each of the acute angle of the right triangle. Include the formula for each function and simplify all radicals. No decimals sin B = cos B = tan B = B 4 sin A = cos A = tan A = 4 2 4 A

7. Find the missing side then write the trig ratios of sin, cos and tan for each of the acute angles. Include the formula and simplify all radicals. 5 1. Use a2 + b2 = c2 to find missing side. 2. Label hyp., opp, adj 3. Write the 3 trig ratios: sin θ = o sin β = o h h cos θ = a cos β = a h h tan θ = o tan β = o a a β θ 13

8. Find the missing side then write the trig ratios of sin, cos and tan for each of the acute angles. Include the formula and simplify all radicals. 12 β 1. Use a2 + b2 = c2 to find missing side. 2. Label hyp., opp, adj 3. Write the 3 trig ratios: sin θ = o sin β = o h h cos θ = a cos β = a h h tan θ = o tan β = o a a θ 8

9. Find the missing side then write the trig ratios of sin, cos and tan for each of the acute angles. Include the formula and simplify all radicals. 17 θ 1. Use a2 + b2 = c2 to find missing side. 2. Label hyp., opp, adj 3. Write the 3 trig ratios: sin θ = o sin β = o h h cos θ = a cos β = a h h tan θ = o tan β = o a a β 15

10. In a right triangle θ and β are acute. Find the sin θ, tanθ, sin β, cos β and tan β if cos θ = 3 7 • Draw a pic. Label known sides. • Find missing side a2 +b2 = c2 • Write the trig functions. Simplify • sin θ = o sin β = o h h • cos θ = a cos β = a h h • tan θ = o tan β = o a a β θ

11. In a right triangle θ and β are acute. Find sin θ, cos θ, sin β, cos β and tan β if tan θ = 7 12 • Draw a pic. Label known sides. • Find missing side: a2 + b2 = c2 • Write the trig functions. simplify • sin θ = o sin β = o h h • cos θ = a cos β = a h h • tan θ = o tan β = o a a β θ

12. Homework Trigonometry of Right Triangles Lesson 1-18 all. Write 5 times each on paper a. Pythagorean Theorem b. sine ratio c. Cosine ratio d. tangent ratio e. SohCahToa