SOLUTION: If sin θ = 8/17, find two possible values of (tan θ + sec θ).

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Question 1118984: If sin θ = 8/17, find two possible values of (tan θ + sec θ).
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
The drawing below shows the situation for Q1 (ignore the labeling on the x and y axes… the triangles are not to scale).


+x+=+sqrt%2817%5E2+-+8%5E2%29+=+sqrt%28225%29+=+15+
+tan%28theta%29+=+8%2F15+
+sec%28theta%29+=+1%2Fcos%28theta%29+=+1%2F%2815%2F17%29+=+17%2F15+
+tan%28theta%29+%2B+sec%28theta%29+=+8%2F15+%2B+17%2F15+=+25%2F15+=+highlight%28+5%2F3+%29+
The other angle is in Q2 (where +sin%28pi-x%29+=+sin%28x%29+ ) so the sine value is still 8/17 (i.e. positive) but the tan & sec values are both negative, resulting in +highlight%28-5%2F3%29+ To visualize, flip the triangle across the y-axis where x<0, and notice theta is still measured counter-clockwise from the positive x-axis but now ends in Q2: