if tan θ = 2/5 for 0< θ <360^2, find the values of sin θ
Obviously solving equations isn't very familiar to you. So here we go:
Multiply both sides of the equation by the complete square-root:
Square both sides:
Expand the bracket:
Collect like terms on one side:
Divide both sides by :
Calculate the square root at both sides:
Due to the squaring in step #2 you'll get 2 solutions of this equation:
You must check if one or both are valid.
tangent function is positive in quadrants I and III. So, the hypotenuse is equal to square root of (5^2 + 2^2) = square root of 29. Then sin theta is equal to + 2/(sqrt of 29) and - 2/(sqrt of 29), because for sin theta, positive in quadrant I and negative in quadrant III.
Hello, deej813!
Since is positive, is in Quadrant 1 or 3.if , find the values of
We have: .
Assume is an acute angle.
Then is in a right triangle with: .
Pythagorus says: .
In Quadrant 1, we have: .
. . Hence: .
In Quadrant 3, we have: .
. . Hence: .
Therefore: .