Evaluate the sine, cosine, and tangent of each of the following angles without using a calculator: `300^0,-405^0,(7pi)/6,(11pi)/4dot`

Find the reference angles corresponding to each of the following angles. It may help if you sketch theta in standard position. (i) theta=-230^0 (ii) (31pi)/9 (iii) theta=640^0

Evaluate int_(0)^(pi)(sin 6x)/(sinx) dx .

Evaluate the definite integrals int_(0)^(pi/4)tanxdx

Evaluate each of the following trigonometric functions: (a) cos.(4pi)/3" (b) "tan(-210^@)" (c ) " cosec.(11pi)/4

Find the locus of the point of intersection of tangents to the ellipse if the difference of the eccentric angle of the points is (2pi)/3dot

If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle, then find the radius of the circle.

Evaluate the following integrals using properties of integration : int_(0)^(2pi) sin ^(4) x cos^(3) x dx

Evaluate int_(0)^(pi//6) cos^(7) 3x dx