Calcupedia

Trig Identities Calculator

Math

Verify the Pythagorean trigonometric identities for a given angle.

Ad · Billboard
-100,000100,000

sin^2(theta) + cos^2(theta)

1.000000

Always equals 1, the fundamental Pythagorean identity.

1 + tan^2(theta)

1.567844

Always equals sec^2(theta).

1 + cot^2(theta)

2.761048

Always equals csc^2(theta).

Share result
Reload calculator
Clear inputs

Found this calculator useful?

From Scratch To $10K/Month In 60 Days

This is a proven money making system that takes students by the hand to make at least $10,000 per month, every month. Students get 12 weeks of guided coaching in addition to the "MPS Super Funnel" and tools.

We value your privacy and promise not to sell or misuse your information. Here's our privacy policy.

Calculator Stats

Odeh Ahwal

Creators

Odeh Ahwal
Reviewed and verifiedThis calculator was reviewed and verified by the Calcupedia due diligence team.

0people find this calculator helpful

Views

Helpful

Saved

Embeds

Like
Share
Embed this calculator
Cite
Save
Ad · 300×250
Ad · 300×250

Frequently Asked Questions

What are the Pythagorean identities?

Three related identities, all derived from the Pythagorean theorem applied to the unit circle: sin^2(theta) + cos^2(theta) = 1, 1 + tan^2(theta) = sec^2(theta), and 1 + cot^2(theta) = csc^2(theta).

Why does sin^2(theta) + cos^2(theta) always equal 1?

On the unit circle, sine and cosine are the y and x coordinates of a point exactly 1 unit from the origin, so by the Pythagorean theorem, x^2 + y^2 = 1^2 for every angle.

How are the other two identities derived from the first?

Dividing every term of sin^2(theta) + cos^2(theta) = 1 by cos^2(theta) gives 1 + tan^2(theta) = sec^2(theta). Dividing instead by sin^2(theta) gives 1 + cot^2(theta) = csc^2(theta).

Spot a mistake? Tell us what's wrong.

Don't see what you need?

Request a calculator. The most-requested ones get built first in our monthly batch.

Request a calculator

Want this calculator on your website?

Embed the Trig Identities Calculator on any site — no code needed. Customize colors, remove branding, and track usage.

Embed it free →
Embed on any platform — Next.js, React, Vue.js, PHP, Laravel, Shopify, Wix, Webflow, Squarespace, and more