Math help please show me how to figure these out!!

1.Find the value of the tangent for angle A. AngleC=90deegres side b =8 side c=12.

2. Find the value of the secant for angle A.
AngleC=90deegres side b=3 side a=2.24

3.if cot =0.85, find tan

4.find cos(-270) deggres

5.find the exact value of sec 300deegres

6.find the value of csc for angle A in standard position if the point at (5,-2) lies on its terminal side.

7.suppose (A) is an angle in standard position whose terminal side lies in quadrant . If sin(A)=12/13,find the value of sec(A)

1. Find the value of the tangent for angle A. Angle C = 90 degrees side b =8 side c=12.

Draw a right triangle ABC with C = 90°, b = 8 and c = 12 (hypotenuse). (the triangle should be drawn such that the angles and their respective opposites sides are of the same letters. A - a, B - b, C - c)

using Pythagorean Theorem,
a^2 = c^2 - b^2
a^2 = 12^2 - 8^2
a^2 = 144 - 64
a^2 = 80
a = 4sqrt(5); note:sqrt means square root

tan A = a/b
tan A = 4sqrt(5)/8
tan A = 1.11803 ans


2. Find the value of the secant for angle A. Angle C = 90 degrees side b=3 side a=2.24

The solution here is very similar to No. 1. Solve for the hypotenuse c using Pythagorean Theorem
secA = c/b


3. If cotθ =0.85, find tanθ

The cotangent function and the tangent function are reciprocal functions. that is,
cotθ = 1/tanθ

therefore,
tanθ = 1/cotθ
tanθ = 1/0.85
tanθ = 1.17647 ans


4. Find cos(-270) degrees

Note: by convention, a POSITIVE angle rotates in a COUNTERCLOCKWISE direction and a NEGATIVE angle rotates in a CLOCKWISE direction. it is important to remember that the positive (+) or negative (-) sign only indicates the DIRECTION of the rotation.

so from the 0° and rotating in a clockwise direction, - 270° is equal to 90°. (you can visualize this by drawing a Cartesian Coordinate and the +x ray indicating 0°.