Expression

There are 3 problems. The first and second problem are with the dotted lines both are division problems. I am looking for the expression for each. 1) Sin(x + B) + cos( x - B) --------------------------- = Cos(x + B) - sin(x - B) 2.) Tan2x + sin2x = ----------------- ...continues

Polar coordinates

x and y represents rectangular coordinates. What is the given equation using polar coordinates (r, theta). x^2 = 4y

Dot product

If v = i - j and w = i + j, find the dot product v * w and the cosine of the angle between v and w.

Proving Trigonometric Identities

Prove sec 2A + tan 2A = (cos A + sin A)/ (cos A - sin A) Express this as a sum of 2 trigo functions 2(siny)(sin5y) Prove (sin2A)^2 - (sinA)^2 = (sinA)(sin3A)

Simple Multiple Angle Formula Solutions using De Moivre's Theorem and Euler's Relation

The double angle formulae are easy to learn: Sin 2x = 2 sin x cos x Cos 2x = (cos x)^2 - (sin x)^2 but working out Cos 4x say in terms of cos x and sin x by using identities such as Cos(A + B) = Cos A Cos B - Sin A Sin B is laborious. Find a simple method to work out any multiple angle formula, using De Moivre' ...continues

Pythagorean Identities (a) (sin x)^2 + (cos x)^2 = 1 (b) 1 + (tan x)^2 = (sec x)^2 (c) 1 + (cot x)^2 = (cosec x)^2

Important Formulas and their Explanations (VI): Identities of Plane Trigonometry Pythagorean Relation Pythagorean Identities ...continues

Trigonometry : Height and Distance of a Cloud Given Location of its Reflection

The angle of elevation of a cloud from a point X m above a lake is A and the angle of depression of its reflection in the lake is 45 degrees. Find the height of cloud?

Find the equation of a circle that touches two lines and another circle.

Find an equation of the circle which touches the straight-lines x + y = 2 and x - y = 2 and touches the circle x2 + y2 =1?

Solving Trigonometric Equations

Solve each equation for exact solutions in the interval [0, 360]. Use either an algebraic method or a graphical method. 2 sin x -1 = csc x

Sum Identity for Tangent

Find the exact value of the expression using the provided information. Find tan (B + C) given that sin C = 1/4, with C in quadrant II, and sin B = -1/2, with B in quadrant IV.