Given sin x=-1/8 and tan x <0, find sin 2x.

Given sin x=-1/8 and tan x <0, find sin 2x.

Find sin 2x Without Using a Calculator

Given sin x=-1/8 and tan x < 0, find sin 2x (without using a calculator).

How do you find the length of the hypotenuse of a triangle?

How do you find the length of the hypotenuse of a triangle?

Solve Trigonometric Equations

Solve for x: sin x = cos x Solve for x: cos x - 6 sec x = 1 Both are 0 is less than or equal to x and x is less than or equal to 2 Pi

polar coordinates

The polar coordinates of a point (-1, -pi/3), find the rectangular coordinates for that point.

Complex Number : Write in standard form.

Write the expression i^6-5 in the standard form a + bi

Vectors

If v=3i-4j, find ||v||

Trigonometric Identities

I have a attachment of 2 problems of which I am trying to solve. For both of these problem, I am to derive an expression. Derive a Trigonometric expression. Please see attached.

Trigonometric Expression

1) 2 tan (theta /2)= 2) 2 tan theta Sin ^2 (theta /2)= 3) 2 Cos (45 + x) Cos (45-x)= 4) (Sin 3 x - 3 Sin x )/ ( Cos 3 x + 3 Cos x) = 5) 2 tan (theta /2) / { 1 + tan ^2 (theta /2) } = 6) Find the least positive value of theta such that tan (45+ theta ) - 3 tan theta =2

Simplify Seven Trigonometric Expressions

1. [sin(x+b) + cos(x+b)]/[cos(x+b)-sin(x+b)]= 2. cos^2(x+b)-cos^2(x-b)= 3. tan x + cot 2x = 4. tan (45 + x) -tan (45 -x)= 5. tanx - cotx + cot 2x = Plus two more...