Evaluating, Solving and Continuity of Trigonometric Expressions, Equations and Functions (10 Problems)
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PART 1:
1. Simplify the expression tan( arccos(x/5))
Your final answer is not supposed to contain any tirgonometric or inverse trigonometric functions.
2. Evaluate the following expressions. Your answer must be an angle -pi/2 <= theta <= pi in radians, written as a multiple of pi.
arcsin(sin(pi/6)) = ___ pi
arcsin(sin(5pi/4)) = ___ pi
arccos(cos(2pi/3)) = ___ pi
arccos(cos(-7pi/4)) = ___ pi
3. Solve the equation in the interval [0, 2pi].
(sin(x))^2 = 1/16
x = ______
Your final answer is not suppose to contain any trigonometric or inverse trigonometric functions.
PART 2:
Match expressions from Group A to group B and show reasoning.
A. tan (arcsin(x/4))
B. cos (arcsin(x/4))
C. (1/2)sin(2arcsin(x/4))
D. sin(arctan(x/4))
E. cos(arctan(x/4))
1. x/(sqrt(16 + x^2))
2. 4/(sqrt(16+x^2))
3. (x/16)(sqrt(16-x^2))
4. x/(sqrt(16 - x^2))
5. sqrt(16 - x^2) / 4
For what value of the constanct c is the function f continuous on (-infinity, infinity) where
f(z) = cz + 1 if z is between - infinity and four
or = cz^2 - 1 is between four and infinity
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Ten problems regarding Evaluating, Solving and Continuity of Trigonometric Expressions, Equations and Functions are solved.
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