Identity Intel Key

Teacher Reference: Solution Dossier

RESOURCE: ANSWER KEY

SECURITY LEVEL: INSTRUCTOR ONLY

Phase 1: Basic Intercepts

1. \( \csc \theta \cdot \sin \theta \)

Result: 1

Rational: \( \frac{1}{\sin \theta} \cdot \sin \theta = 1 \)

2. \( \tan x \cdot \cos x \)

Result: \( \sin x \)

Rational: \( \frac{\sin x}{\cos x} \cdot \cos x = \sin x \)

3. \( \frac{1}{\sec A} \)

Result: \( \cos A \)

Phase 2: Squared Signals

4. \( \sin^2(42^\circ) + \cos^2(42^\circ) \)

Result: 1

5. \( 1 + \tan^2 \beta \)

Result: \( \sec^2 \beta \)

6. \( \frac{1 - \cos^2 x}{\sin x} \)

Result: \( \sin x \)

Rational: \( \frac{\sin^2 x}{\sin x} = \sin x \)

Phase 3: Compound Codes

7. \( \sin(A + B) \)

Result: \( \sin A \cos B + \cos A \sin B \)

8. \( \cos(\alpha - \beta) \)

Result: \( \cos \alpha \cos \beta + \sin \alpha \sin \beta \)

9. \( \cos(75^\circ) = \cos(45^\circ + 30^\circ) \)

Result: \( \frac{\sqrt{6} - \sqrt{2}}{4} \)

Work: \( \cos 45 \cos 30 - \sin 45 \sin 30 = \frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2}\cdot\frac{1}{2} = \frac{\sqrt{6} - \sqrt{2}}{4} \)

Phase 4: Frequency Doublers

10. \( \sin(2\theta) \)

Result: \( 2\sin \theta \cos \theta \)

11. \( \cos(2x) \) in terms of \( \sin x \)

Result: \( 1 - 2\sin^2 x \)

12. If \( \sin u = \frac{3}{5} \) (Quad I), find \( \sin(2u) \)

Result: \( \frac{24}{25} \)

Work: \( \cos u = \frac{4}{5} \). Then \( \sin(2u) = 2(\frac{3}{5})(\frac{4}{5}) = \frac{24}{25} \).

Identity Intel Answer Key

Identity Intel Answer Key

Similar Materials

Navigator Mission Cards

Danielle Burham

Cosmic Symmetry Quiz

Danielle Burham

Global Grid Reference Sheet

Danielle Burham

Pattern Detective Worksheet

Danielle Burham

Cosmic Reference Sheet

Danielle Burham

Master Key Teacher Guide

Danielle Burham

Navigator Grid Worksheet

Danielle Burham

Cosmic Symmetry Slides

Danielle Burham

Navigator Briefing Teacher Guide

Danielle Burham

Cosmic Patterns Worksheet

Danielle Burham

Cosmic Compass Slides

Danielle Burham

Inequality Practice Worksheet

COURTNEY SCHERER

Inequality Guided Notes

COURTNEY SCHERER

Inequality Steps Anchor Chart

COURTNEY SCHERER

Factoring Forge Answer Key

klockaby

Factoring Forge Worksheet

klockaby

Factoring Slides

klockaby

Quadratic Blueprint Organizer

klockaby

Review Quiz Worksheet

V Lundgren

The Percentage Edge Exit Ticket

V Lundgren

The Percentage Edge Worksheet

V Lundgren

Part and Parcel Exit Ticket

V Lundgren

Part and Parcel Worksheet

V Lundgren

Cents and Sense Exit Ticket

V Lundgren

Cents and Sense Worksheet

V Lundgren

Big Number Exit Ticket

V Lundgren

Big Number Worksheet

V Lundgren

Review Quiz Answer Key

V Lundgren

The Percentage Edge Answer Key

V Lundgren

Part and Parcel Answer Key

V Lundgren

Cents and Sense Answer Key

V Lundgren

Big Number Answer Key

V Lundgren

The Percentage Edge Slides

V Lundgren

Part and Parcel Slides

V Lundgren

Cents and Sense Slides

V Lundgren

Big Number Slides

V Lundgren

Guide du Maître Labo 2

Enseignante

Billet de Sortie Corrigé

Enseignante

Cartographie Labo Corrigé