Trigonometry By: Jayden and Mr.D.

What is Trigonometry？ Trigonometry is the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. And Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

Finding missing Angles Finding missing Angles. Example: Find the Missing Angle "C" Angle C can be found using angles of a triangle add to 180°: So C = C A B 34°

Finding missing Angles Finding missing Angles. Example: Find the Missing Angle "C" Angle C can be found using angles of a triangle add to 180°: So C = 180°- 90°- 34°= 56° 34°

Right Angled Triangle And we give names to each side:  To use Trigonometry, you must have a right-angled triangle. The right angle is shown by the little box in the corner. We usually know another angle θ (or we can find it using trigonometry). And we give names to each side: Adjacent is adjacent (next to) to the angle θ Opposite is opposite the angle θ the longest side is the Hypotenuse

Sine, Cosine and Tangent Trigonometry is good at find a missing side or angle in a triangle. The special functions Sine, Cosine and Tangent help us! They are simply one side of a right-angled triangle divided by another. For any angle "θ":                                      (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)   Sine Function: sin(θ) = Opposite / Hypotenuse Cosine Function: cos(θ) = Adjacent / Hypotenuse Tangent Function: tan(θ) = Opposite / Adjacent

Example: What is the sine of 35°? Using this triangle: sin(35°) = ?? NOTE: Leave as a fraction or go to 4 decimal places.   

Example: What is the sine of 35°? Using this triangle (lengths are only to one decimal place): sin(35°) = Opposite / Hypotenuse = 2.8/4.9 = 0.5714   

Example: What is the sine of 35°? Using this triangle (lengths are only to one decimal place): sin(35°) = Opposite / Hypotenuse = 2.8/4.9 = 0.57    Now look on your “Trig Tables” sheet…

Trigonometric Ratios Find the given trigonometric ratio. The answer can be in fraction or decimal form. Example: Find the cos Z V 65 cm 16cm O 63cm Z

Trigonometric Ratios Find the given trigonometric ratio. The answer can be in fraction or decimal form. Example: Find the cos Z V 65 cm 16cm O 63cm Z cosZ = Adj Hyp

Trigonometric Ratios Find the given trigonometric ratio. The answer can be in fraction or decimal form. Example: Find the cos Z V 65 cm 16cm O 63cm Z cosZ = Adj = 63cm = 0.9692 Hyp 65cm

Solving Triangles A big part of Trigonometry is Solving Triangles. "Solving" means finding missing sides and angles. Example: Find the missing side“AB" A 5 cm 37° B

Cosecant, Secant and Cotangent Other functions – Cosecant, Secant and Cotangent Other Functions (Cotangent, Secant, Cosecant) Similar to Sine, Cosine and Tangent, there are three other trigonometric functions which are made by dividing one side by another:                                        Cosecant Function: csc(θ) = Hypotenuse / Opposite Secant Function: sec(θ) = Hypotenuse / Adjacent Cotangent Function: cot(θ) = Adjacent / Opposite

SWYK TIME!!!