Question

Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has

length 6 and the side opposite angle A has length 10.
10
Figure 1
Sin A=
cos A=
tan A=
sec A=
csc A=
cot A=

Answer 1

1. sinA = (5√34)/34

2. cosA = 3√34)/34

3. tan A = 5/3

4. sec A = √34/3

5. cosec A = √34/5

6. cot A = 3/5

What are trigonometric ratio?

Trigonometric ratios express the relationships between angles and sides in a right triangle.

Common ratios include sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent).

These ratios are fundamental in trigonometry, aiding in the calculation of angles and side lengths.

To find the trig ratios of A , we need to find the hypotenuse, using Pythagorean theorem

Hyp = √10² + 6²

Hyp = √ 136 = 2√34

1. SinA = opp/hyp

= 10/2√34 = 5/√34 = (5√34)/34

2. cosA = adj/hyp

= 6/2√34 = (3√34)/34

3. tan A = opp/adj = 10/6 = 5/3

4. secA = hyp/adj = 2√34/6 = √34/3

5. cosec A = hyp/opp = 2√34/10 = √34/5

6. cot A = adj/opp = 6/10 = 3/5