# If #cos A = 5/13#, how do you find sinA and tanA?

##### 6 Answers

In this way:

(Without further information about the angle

and

#### Explanation:

The basic trig functions are defined in a right-angled triangle as:

So, as we are given

in this specific right-angled triangle,

the side adjacent to

Using Pythagoras' Theorem.

So now the side opposite

Now we can give the trig ratios as:

From these,we can find that

angle

#### Explanation:

There are 2 opposite values of sin A, because, when cos A =

the arc (angle) A could be either in Quadrant 1 or in Quadrant 4.

There are also 2 opposite values for tan A

#### Explanation:

If we have a right triangle where

With the Pythagorean Theorem, we find that the opposite side is

From this, we see that

Hope this helps!

#### Explanation:

Unless otherwise restricted,

A = 2kpi +- arccos ( 5/13 ) = 2kpi +- 67.38^o#

# k = 0, +-1, +-2, +-3, ...3

And so,

#### Explanation:

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2.

If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are co-prime (that is, they have no common divisor larger than 1).

The best known triple is 3-4-5, with 5-12-13 being the next most recognised.

Any triangle composed of sides of lengths that match the Pythagorean triple will be a right triangle.

That means our triangle has a 90 degree angle for angle C.