How do I find the quadrant in which angle thada may lie if cos thada > 0 and tan thada < 0?
cos(theta)>0 in Q1, and Q4.
tan(theta)<0 in Q2, and Q4.
Q4 satisfies both conditions. Therefore, angle theta lies in Q4.
To find the quadrant in which an angle thada may lie given that cos thada > 0 and tan thada < 0, you can follow these steps:
Step 1: Recall the basic properties of trigonometric functions in different quadrants:
- In the first quadrant (Q1), all trigonometric functions (sin, cos, tan) are positive.
- In the second quadrant (Q2), only sin and cosec are positive.
- In the third quadrant (Q3), only tan and cot are positive.
- In the fourth quadrant (Q4), only cos and sec are positive.
Step 2: Given that cos thada > 0, we can determine that thada lies in either Q1 or Q4, as these are the only quadrants where cos is positive.
Step 3: Given that tan thada < 0, we can determine that thada lies in either Q2 or Q4, as these are the only quadrants where tan is negative.
Step 4: Combining the information from steps 2 and 3, we can conclude that thada must lie in Q4, as it is the common quadrant where both conditions are satisfied.
So, to answer your question, the angle thada may lie in the fourth quadrant (Q4) based on the given conditions.