Pre-Calculus Unit 4 Video Resources

Unit 4:  Analytic Trigonometry and Trigonometric Applications

Activity 21

Trigonometric Identities

21-1 Learning Targets:

·       Define the reciprocal and quotient identities.

·       Use and transform the Pythagorean identity.

21-2 Learning Targets:

·       Simplify trigonometric expressions.

• Verify trigonometric identities.

Trigonometric Identities

Pythagorean trig identity from soh cah toa

Pythagorean trig identity from unit circle

Using the Pythagorean trig identity

Simplifying Trigonometric Expressions

Examples using pythagorean identities to simplify trigonometric expressions

Activity 22

Identities and Equations

22-1 Learning Targets:

·       Use the unit circle to write equivalent trigonometric expressions.

·       Write cofunction identities for sine and cosine.

22-2 Learning Targets:

·       Use trigonometric identities to solve equations.

·       Solve trigonometric equations by graphing.

Activity 23

Multiple Angle Identities

23-1 Learning Targets:

·       Model a sound wave with a trigonometric function.

·       Derive an expression for the cosine of a difference.

23-2 Learning Targets:

·       Write the sum and difference identities for sine, cosine, and tangent.

·       Use sum and difference identities to find exact values of a trig function.

·       Derive the double angle and half angle identities.

23-3 Learning Targets:

·       Use trigonometric identities to solve equations.

Verify trigonometric identities

Exploring Sums of Trig  Functions

Applying angle addition formula for sin

Angle addition formula with cosine

Another example using angle addition formula with cosine

Sine of non special angle

Cosine addition identity example

Proof of angle addition formula for sine

Proof of angle addition formula for cosine

Double Angle Formulas

Double angle formula for cosine example

Activity 24

Law of Cosines

24-1 Learning Targets:

·       Use trigonometry to draw and interpret diagrams for a model.

·       Write a trigonometric function for a real-world situation

·        

24-2 Learning Targets:

·       Write equations for the Law of Cosines using a standard angle.

Apply the Law of Cosines in real-world and mathematical situations.

Law of Cosines

Law of cosines

Law of cosines to determine grade

Law of cosines for star distance

Proof of the law of cosines

Activity 25

Law of Sines

25-1 Learning Targets:

·       Calculate the bearing of a flight.

·       Derive and use the Law of Sines.

·       Find unknown sides or angles in oblique triangles.

25-2 Learning Targets:

·       Determine the number of distinct triangles given certain criteria.

Use the Law of Sines to solve triangles with unknown sides or angles.

Law of Sines

Law of sines

Law of sines for missing angle

Proof: Law of sines