Question

Find value without calculator or table (in radians)

csc^-1 (2/squareroot2), sec^-1 (2/squareroot2)

Answer 1

FOr this type of question, you have to remember the unit circle.When converting these back to sin and cos, the ordered pair if \[(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})\]What angle measure on the unit circle has this ordered pair?

Answer 2

pi/4

Answer 3

never mind..dont know

Answer 4

\[\huge\text{You got it! }\frac{π}{4}\text{ is correct!}\]

Answer 5

yeah but how do I show work on test??

Answer 6

You can't really show much work...if you want to show work, you couls show how sec and csc are reciprocals of sin and cos which is how I got the √2/2 stuff. Then you could draw the first quadrant of the unit circle including the value of π/4.

Answer 7

Is there a trick for memorizing unit circle??

Answer 8

Well really, you just have to focus on the first quadrant. The using logic, you can remember the other three using the first.
Yeah. The two values I showed are the same because they are reflected, but since it's in quadrant 2, the x-value is negative.

Answer 9

Also remember
All
Students
Take
Calculus

Answer 10

It represents the values out of sin, cos, and tan are positive in each quadrant.
All (Quadrant I)
Sin (Quadrant II)
Tan (Quadrant III)
Cos (Quadrant IV)
See?

Answer 11

Yep thanks

Answer 12

np :)