Question

Given that sin =3/5and angle is obtuse,without using mathemical tables or calculators, find the values of cos angle and tanangle

Answer 1

To find the values of cos angle and tan angle, substitute the given sin value into the Pythagorean identity and solve for cos angle. Then, use the identity tan(angle) = sin(angle) / cos(angle) to find the value of tan angle.

Step-by-step explanation:

To find the values of cos angle and tan angle, we can use the Pythagorean identity:
`sin^2(angle) + cos^2(angle)`= 1. Given that sin(angle) = 3/5, we can substitute this value into the equation:

`(3/5)^2 + cos^2(angle)` = 1

Simplifying the equation, we get:

`9/25 + cos^2(angle) = 1`

To solve for cos angle, we subtract 9/25 from both sides and take the square root:

cos(angle) = √(1 - 9/25) = √(16/25) = 4/5

To find the value of tan angle, we can use the identity: tan(angle) = sin(angle) / cos(angle). Substituting the values, we get:

tan(angle) = (3/5) / (4/5) = 3/4