Trigonometry
Not what you're looking for?
1) Verify the following identities :
a) sin(x+y)cos(x-y) + cos(x+y)sin ( x-y) = sin 2x
b) cos2x = [cot^2 (x-1 )] / [ cot^2 (x+1) ]
2) Derive the identity for sin 3x in terms of sin x
3) Using the double-angle formula, find sin 120° .
4)Simplify the following expressions so that they involve a function of only one angle:
a) (sin 80° - sin 10° ) / (sin 80° + sin 10°)
b) (sin 130° + sin 20°) / (cos 130° + cos 20 °)
A) Use logarithms and the law of tangents to solve the triangle ABC,
given that a=21.46 ft, b=46.28 ft, and C=32° 28' 30"
B) Solve the triangle for which the given parts are :
a=27, b=21, and c=24.
Purchase this Solution
Solution Summary
Neat, step-by-step solutions that verify the given identities are provided for all the plane trigonmetry questions.
Solution Preview
The solution file is attached.
1) Verify the following identities :
a) sin(x+y)cos(x-y) + cos(x+y)sin ( x-y) = sin 2x
LHS = sin(x + y) cos(x - y) + cos(x + y) sin(x - y)
= sin A cos B + cos A sin B [where x + y = A and x - y = B]
= sin (A + B)
= sin[(x + y) + (x - y)]
= sin 2x
= RHS
b) cos2x = [cot^2 (x-1 )] / [ cot^2 (x+1) ]
There appears to be some error in this question. This identity does not hold for x = 1 (for example).
When x = 1, LHS = cos (2 * 1) = cos 2 (finite), whereas,
RHS = [cot^2 (1 - 1)]/[cot^2 (1 + 1)] = cot^2 (0) / cot^2 (2), which is undefined.
[Please check again at your end.]
2) Derive the ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.