Let theta be an angle in standard position, sin theta < 0, cos theta > 0. Name the quadrant in which theta lies.

Let theta be an angle in standard position, sin theta < 0, cos theta > 0. Name the quadrant in which theta lies.

Question
Trigonometric Functions
asked 2021-02-09
Let theta be an angle in standard position, \(\displaystyle{\sin{\theta}}{<}{0},{\cos{\theta}}{>}{0}\). Name the quadrant in which theta lies.

Answers (1)

2021-02-10
as we know that:
(1)in first quadrant all trigonometric functions are positive.
(2)in second quadrant sine and cosecant trigonometric functions are positive and rest trigonometric functions are negative.
(3)in third quadrant tangent and cotangent trigonometric functions are positive and rest trigonometric functions are negative.
(4)in fourth quadrant cosine and secant trigonometric functions are positive and rest trigonometric functions are negative.
as \(\displaystyle{\sin{\theta}}{<}{0},{\cos{\theta}}{>}{0},\)
therefore we can say that the angle theta lies in the fourth quadrant.
therefore, the quadrant in which theta lies is fourth quadrant.
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