The required value of sinΦ = -3 / 5 and Quadran III and Quadrant IV.
Given,
cos 0 = 4 / 5 and sin 0 < 0.
What are trigonometric equations?
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
cosΦ = 4/5 = base/hypotenuse
base(b) = 4 and hypotenuse(h) = 5, perpendicular(p) = ?
Using Pythagorean theorem
h² = p² + b²
5² = p² + 4²
p² = 25 - 16
p = √ 9
p = 3
now
sinФ = p / h = -3/5 ( since sinФ < 0 given )
And in quadrant 3 and 4 values of the sin is always negative.
Thus, the required value of sinΦ = -3 / 5 and Quadran III and Quadrant IV.
Learn more about trigonometry equations here:
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To identify the quadrant of the terminal side of 0 and find sin 0 to be determined.
