Trigonometric Identities & Solving Trig Equations – Grade 12 / First-Year Math Notes

$4.05

Preview 1 out of 3 pages

Class notes

Trigonometric Identities & Solving Trig Equations – Grade 12 / First-Year Math Notes

0.0

(0 reviews)

- sold

3 pages

2025/2026

Institution

Course

Preview 1 out of 3 pages

This document provides comprehensive Grade 12 and first-year pre-calculus notes on trigonometric identities and solving trigonometric equations. It includes all fundamental identities, clear rules for proving identities, step-by-step worked examples, and methods for solving equations within a given interval. Designed for Advanced Functions (MHF4U) and equivalent courses, these notes are perfect for exam preparation, homework help, and concept review.

Content preview

GRADE 12 TRIGONOMETRIC IDENTITIES &
SOLVING TRIGONOMETRIC EQUATIONS
Complete study notes with identities, strategies, and worked examples.

1. Basic Trigonometric Ratios
For an angle θ:

sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
tanθ = opposite / adjacent

Reciprocal Ratios:
cosecθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ

2. Fundamental Identities
Pythagorean Identities:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ

Quotient Identities:
tanθ = sinθ / cosθ
cotθ = cosθ / sinθ

Reciprocal Identities:
sinθ = 1/cosecθ
cosθ = 1/secθ
tanθ = 1/cotθ

3. Proving Trigonometric Identities
Goal: Show that LHS = RHS.

Rules:
• Work on ONE side only

Document information

Study: 12th Grade
School year: 1
Uploaded on: December 18, 2025
Number of pages: 3
Written in: 2025/2026
Type: Class notes
Professor(s): Mr shawn
Contains: All classes

Report Copyright Violation

$4.05

Written by students who passed

Immediately available after payment

Read online or as PDF

trigonometric identities
solving trig equations
advanced functions
grade 12
pre calculus
sine
cosine
tangent
factoring trig equations
proving trig identities

Why students choose Stuvia

Created by fellow students, verified by reviews

Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.

Didn't get what you expected? Choose another document

No worries! You can instantly pick a different document that better fits what you're looking for.

Pay as you like, start learning right away

No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.

“Bought, downloaded, and aced it. It really can be that simple.”

Alisha Student

Frequently asked questions

Can't I just make this for free with AI?

AI tools give you vast, general information. They don't know your course, your professor, or what actually gets asked in your exam. This document was written by a fellow student who understood the nuances of exactly this course and passed it. You get focused, curated study material, not a generic starting point you still have to rework.

Is this document still relevant for my course?

Every document shows the academic year, the linked textbook, and the institution, so you can check upfront whether it matches your course. Take a look at the free preview too to see if it fits.

What if the document isn't what I hoped?

No worries! If you change your mind within 14 days of purchase and have not downloaded the document yet, you will get a refund. Your purchase is completely risk-free.

Who am I actually buying from?

Stuvia is a marketplace: you buy directly from the student who created the document. Stuvia handles payment securely and backs every purchase with the free exchange guarantee, so you never take on any risk.

Will I be stuck with a subscription?

No. You pay $4.05 once for this document and nothing more. No subscription, no auto-renewal, no fine print.

What do I get when I buy this document?

You get a PDF that is available immediately after payment. You can read the document online or download it, and it stays accessible through your profile indefinitely.

Why can I trust Stuvia?

4.6 stars on Google and Trustpilot from over 2,000 reviews. In the past 30 days 32796 documents were sold through Stuvia internationally. And we have been doing this for 16 years now. Every document also shows its rating and how many times it has been sold.

Trigonometric Identities & Solving Trig Equations – Grade 12 / First-Year Math Notes

Content preview

Document information

More like this

Why students choose Stuvia

Created by fellow students, verified by reviews

Didn't get what you expected? Choose another document

Pay as you like, start learning right away

Working on your references?

Frequently asked questions

Can't I just make this for free with AI?

Is this document still relevant for my course?

What if the document isn't what I hoped?

Who am I actually buying from?

Will I be stuck with a subscription?

What do I get when I buy this document?

Why can I trust Stuvia?

Trigonometric Identities & Solving Trig Equations – Grade 12 / First-Year Math Notes

Content preview

Document information

Browse related subjects

Subjects

Why students choose Stuvia

Created by fellow students, verified by reviews

Didn't get what you expected? Choose another document

Pay as you like, start learning right away

Working on your references?

Frequently asked questions

Can't I just make this for free with AI?

Is this document still relevant for my course?

What if the document isn't what I hoped?

Who am I actually buying from?

Will I be stuck with a subscription?

What do I get when I buy this document?

Why can I trust Stuvia?