If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Trigonometry

### Course: Trigonometry>Unit 2

Lesson 1: Unit circle introduction

# The trig functions & right triangle trig ratios

Sal shows how, for acute angles, the two different definitions of the trigonometric values (SOH CAH TOA and the unit circle definition) result in the same values. Created by Sal Khan.

## Want to join the conversation?

• Hard to pay attention to, all I see is letters and those don't add or divide. they are not numbers. letters everywhere and confused
• Think of them as numbers with no identity, they are called variables.
• Still kinda confused on the fractions on the unit circle, hard to remember.
• is to illustrate the fact their either the unit circle or a plain triangle can be used to find the same trig ratios
• The video doesn't really help with the practice exercises, i've seen similar complaints below that are from a year ago and the issue has not been fixed since then... i'm jumping to the next section for now but please fix the issue, so we can come back and finish this section.

I've got two exercises out of five right in a row and as soon as i think to have got it, something blows up, it's so frustrating...
• In the unit circle, can we imagine the hypotenuse in any rt angle triangle is a straight line on a cartesian plane and so it's equation is y=mx+c, and, since c = zero, m=y/x - the equation for tan(theta). So tan(theta) is the gradient of the hypotenuse?
• Yes, your reasoning is perfectly right. Tangent is defined by the Y ordenade of the point in which the line defined by the angle crosses the x=1 line.
• What does Sal mean by the Unit Circle is an extension of SOH-CAH-TOA? I know what they mean, but how is it an extension?
• In SOH, CAH, TOA, definition of trig functions, we defined the sin,cos etc .
as the ratio of the sides of a triangle. Also, we were only able to find the value of trig functions of angles upto 90 degrees.
But in unit circle definition, the trigonometric functions sine and cosine are defined in terms of the coordinates of points lying on the unit circle x^2 + y^2=1. And unlike the previous definition(SOH, CA...), we are able to find sin,cos.... of all possible angles.
That's how the Unit Circle definition is an extension of SOH,CA.... definition.
• Not much explanation of what the ratios are or how they are used. Just a lot of quick talk. The exercise questions do not follow the lesson and have that bland text-book feel to them when you use hints. Khan Academy has definitely moved away from the simple approach that it was founded on to a more public school diploma chugging factory approach...
• How can I solve for a trigonometric function without using my calculator? What does mathematicians do to solve a sine or inverse sine function in middle ages?
• According to Wikipedia, "Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering."
• So suppose ive been given that sin(theta) is -4/5 and that cos(theta) > 0, how would I find cos(theta) and tan(theta)
• You could use the Pythagorean identity: sin²(θ) + cos²(θ) = 1
First you rearrange that to give an formula for cos(θ) in terms of sin(θ) - which you know.
Then, once you have cos(θ), you can get tan(θ) = sin(θ)/cos(θ)