remember from geo & alg 2!!!

trigonometric functions!

use the triangle below define the six trigonometric functions:

sine: $\sin\theta = \frac{o}{h}$
cosine: $\cos\theta = \frac{a}{h}$
tangent: $\tan\theta = \frac{o}{a}$

example: find all three trig ratios.

you try! find the exact values of the three trigonometric ratios of $\theta$.

1. a right triangle with sides 5, 12, and hypotenuse 13, with angle $\theta$ opposite to the side of length 12.
2. a right triangle abc with sides bc = 3, ac = 4, and hypotenuse ab = 5, with angle a.

Question

remember from geo & alg 2!!!

trigonometric functions!

use the triangle below define the six trigonometric functions:

sine: $\sin\theta = \frac{o}{h}$
cosine: $\cos\theta = \frac{a}{h}$
tangent: $\tan\theta = \frac{o}{a}$

example: find all three trig ratios.

you try! find the exact values of the three trigonometric ratios of $\theta$.

1. a right triangle with sides 5, 12, and hypotenuse 13, with angle $\theta$ opposite to the side of length 12.
2. a right triangle abc with sides bc = 3, ac = 4, and hypotenuse ab = 5, with angle a.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Ratios", "Right Triangle Trigonometry" ], "new_concepts": [], "current_concepts": [ "Trigonometric Ratios", "Right Triangle Trigonometry" ] } ## Identify sides for Question 1 $$ \begin{aligned} &\text{Opposite side to } \theta = 12 \ &\text{Adjacent side to } \theta = 5 \ &\text{Hypotenuse} = 13 \end{aligned} $$ ## Calculate ratios for Question 1 $$ \begin{aligned} &\sin\theta = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{12}{13} \ &\cos\theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{5}{13} \ &\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{12}{5} \end{aligned} $$ ## Identify sides and calculate ratios for Question 2 $$ \begin{aligned} &\text{Opposite side to } A = 3 \ &\text{Adjacent side to } A = 4 \ &\text{Hypotenuse} = 5 \ &\sin A = \frac{3}{5} \ &\cos A = \frac{4}{5} \ &\tan A = \frac{3}{4} \end{aligned} $$ ## Question 1 $$ \begin{aligned} \sin\theta &= \frac{12}{13} \ \cos\theta &= \frac{5}{13} \ \tan\theta &= \frac{12}{5} \end{aligned} $$ ## Question 2 $$ \begin{aligned} \sin A &= \frac{3}{5} \ \cos A &= \frac{4}{5} \ \tan A &= \frac{3}{4} \end{aligned} $$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Ratios" ] }

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QUESTION IMAGE

Question

Explanation:

Identify sides for Question 1

Calculate ratios for Question 1

Identify sides and calculate ratios for Question 2

Answer:

Question 1

Question 2