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1. Find the exact value of y, or state that y is undefined. Y=sin -1 (1) Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression.
Y=sin -1 (1) = [pic]
2. Find the exact value of y or state that y is undefined. Y=cos -1 (-square root 3 over 2) Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression.
Y=cos -1 (-square root 3 over 2) [pic]
3. Find the exact value of y or state that y is undefined. Y = tan -1 square root3 over 3 ) Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression.
Y = tan -1 square root3 over 3 ) [pic]
4. Find the exact value in radians, of y or state that y is undefined. Y=cot -1 (-1) simplify answer. Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression.
Y=cot -1 (-1) [pic]
5. Find the exact value in radians or y or state that y is undefined. Y=sec -1 (2) Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression.
Y=sec -1 (2) [pic]
6. Find the exact value of y or state that y is undefined. Y = csc -1 2 simplify answer. Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression. Type your answer in radians.
Y = csc -1 2 [pic]
7. Find the exact value of y or state that y is undefined. Y=cos (cos -1 (-0.3)) simplify answer, including any radicals. Use integers or fractions for any number in the expression.
Y=cos (cos -1 (-0.3)) = - 0.3
8. Find the exact value of y or state that y is undefined. Y = tan (tan -1 8) simplify answer. Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression. Type your answer in radians.
Y = tan (tan -1 8) = 8
9. Find the exact value of y or state that y is undefined. Y=tan -1 ( tan 9pi/10) simplify answer. Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression. Type your answer in radians.
Y=tan -1 ( tan 9pi/10) [pic]
10. Use a sketch to find the exact value of y. y= cos [tan -1 11/3] simplify answer, including any radicals. Use integers or fractions for any numbers in the expression.
y= cos [tan -1 11/3]
Let [pic] or[pic].
We can draw the following triangle.
[pic]
In the above triangle, [pic].
Hence, [pic]
11. Find the exact value of y or state that y is undefined. Y=sin [tan -1 (-8)] simplify answer, including any radicals. Use integers or fractions for any numbers in the expression.
Y=sin [tan -1 (-8)]
Let [pic] or[pic]
We can draw the following triangle.
[pic]
In the above triangle [pic]
Hence, [pic]
12. Find the exact value of the expression sin ( sin -1 4/5 + tan -1 5/12) type an exact answer in simplified form
sin ( sin -1 4/5 + tan -1 5/12)
Let [pic] and [pic]
We can make the following two triangles representing α and β.
[pic]
Hence, sin ( sin -1 4/5 + tan -1 5/12) = [pic]
[pic]
[pic]
13. Find the exact value of the expression tan[ cos -1 (12/13) + tan -1 (3/5)] type an integer or a simplified fraction. There seems to be mistake in typing. It should be tan[ cos -1 (12/13) + tan -1 (3/4)].
tan[ cos -1 (12/13) + tan -1 (3/4)]
Let [pic] and [pic]
We can make the following two triangles representing α and β.
[pic]
Hence, tan[ cos -1 (12/13) + tan -1 (3/4)] = [pic]
[pic]
14. Use a calculator to find the value of y in radians rounded to two decimal places. Y = cos -1 (-0.28) type your answer in radians. Round 2 decimal places as needed.
Y = cos -1 (-0.28) [pic]
15. Evualate the following expression in terms of x. sin (tan -1 6x) type an exact answer, using radicals as needed.
sin (tan -1 6x) = sinα if tan-16x = α or tan α =6x
Hence, we can make the following triangle.
[pic]
From the above triangle, [pic]
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