University:
East Georgia State College
Course:
MATH 1001 | Quantitative Skills & Reasoning
Academic year:

2021
Views:

498

Pages:

2
Author:

larbiwxcvbn

Algebra 2 Honors Trig Notes Trigonometric Functions of Acute Angles in Right Triangles Sine: opp/hyp = y/r Cosine: adj/hyp = x/r Tangent: opp/adj = y/x Reciprocal Functions Sine: csc = hyp/opp Cosine: sec = hyp/adj Tangent: cot = adj/opp EXAMPLE 1 - Trig Function Values a. Find the values of the six trigonometric functions of an angle θ in standard position whose terminal side passes through the point (12, 5) sinθ = 5/13 cscθ = 13/5 cosθ = 12/13 secθ = 13/12 tanθ = 5/12 cotθ = 12/5 b. If θ is an acute angle and sinθ = 3/5, find cosθ and tanθ. tanθ = 4/3 cosθ = 3/5 Trigonometric Values for Special Angles Geometry Review: Label the special side lengths for a 30-60-90 and 45-45-90 triangle 30°: sinθ = 1/2, cosθ = √3/2, tanθ = 1/√3 = √3/3, cscθ = 2, secθ = 2/√3 = 2√3/3, cotθ = √3 45°: sinθ = √2/2, cosθ = √2/2, tanθ = 1, cscθ = √2, secθ = √2, cotθ = 1 60°: sinθ = √3/2, cosθ = 1/2, tanθ = √3, cscθ = 2/√3 = 2√3/3, secθ = 2, cotθ = 1/√3 = √3/3 **EXAMPLE 2: Find an Unknown Side Length of a Right Triangle** Find the value for x for the right triangle shown. Then find the missing angle and additional missing side. Your answers must be exact - no decimals. **a.** x /| / | 8/ | /| 30° 2 * x/8 = √3/2 * 2x = 8√3 * x = 4√3 **b.** 45° /| / | √2/ | x /| 1 * x/1 = √2/1 * x = √2 **c. Find the value of x** 50 /| / | / | / | /|_ y 30° 30° x+y * 50/y = √3/1 * y√3 = 50 * y = 50/√3 = 50√3/3 * 50/(x+y) = 1/√3 * 50√3 = x + 50√3/3 * 150√3/3 - 50√3/3 = x * x = 100√3/3 **Cofunction Identities** * sinθ = cos(90°-θ) * cosθ = sin(90°-θ) * tanθ = cot(90°-θ) * cotθ = tan(90°-θ) * secθ = csc(90°-θ) * cscθ = sec(90°-θ) **EXAMPLE 3: Cofunction Identities** Use the cofunction identities to find the measure of the acute angle θ. **a.** sinθ = cos 25° * sinθ = cos(90°-25°) * 65° = θ **b.** tanθ = cot 70° * tanθ = cot(90°-70°) * θ = 20°