5.1 Trigonometric Functions of Acute Angles Fri Oct 17 Do Now Solve for x 1) 1^2 + x^2 = 2^2 2) x^2 + x^2 = 1

Quiz Review Retakes by Monday

Trigonometric Ratios Given a right triangle, the lengths of the sides of the triangle are used to define the six trigonometric ratios Sine (Sin) Cosine (Cos) Tangent (Tan) Cosecant (Csc) Secant (Sec) Cotangent (Cot)

Trigonometric Functions Values of an Acute Angle Let be an acute angle of a right triangle, then the 6 trig functions are:

Reciprocal Functions Cosecant, secant, and cotangent are reciprocals of sine, cosine, and tangent respectively

Ex1 If sinx = 12/13, find the other 5 trig function values

Ex 2 Given Tanx = 4/3, find the other 5 trig function values

Ex3 If sinx = 6/7 and x is an acute angle, find the other 5 trig function values

Similar Triangles and Trig If two triangles are similar, their trigonometric function values will be the same Ex: and right triangles Note to self, if time keep going

Closure If cosx = 4/7, find the other 5 trig values HW: p.444 #1-29 odds

5.1 Trigonometric Functions of Acute Angles Mon Oct 20 Do Now Let cscx = 5/4 Find the other 5 trig values

HW Review: p.444 #1-15 odds

Trig Values of 30, 45, 60 deg Using geometry, we can construct right triangles using 30, 45, and 60 degrees, then find the trig values

Right Triangle

Right Triangle

Ex As a hot-air balloon began to rise, the ground crew drove 1.2 mi to an observation station. The initial observation from the station estimated the angle between the ground and line of sight to the balloon to be 30 degrees. Approximately how high was the balloon at that point?

Decimal-Degree and Degree-Minute- Second Form To convert from DMS to decimal degree, – 1) Use 2 nd -> Angle to write degree and minute – 2) Use Alpha -> + sign to write second To convert from decimal degree to DMS, – Use 2 nd -> Angle -> DMS

Ex Convert degrees to DMS and back

Trig Values of other Angles To find the 6 trig values of other angles, we will use the calculator. – Be sure your calculator is in the correct mode Angles can be expressed in degrees or radians – Round to at least 3 decimal places

Finding the Angle We use inverse trig functions (has a -1) to find the angle Ex: Find the angle whose sine value is

Ex A paint crew has purchased new 30ft extension ladders. They extend the ladder to 25 ft and position the base 6.5 ft away from the wall. What angle does the ladder make with the ground?

Cofunction Identities Since the 2 acute angles in a right triangle will always be complementary, the following identities are a result

Ex Given sin 18 deg = , cos 18 deg = , and tan 18 deg = , find the 6 trig function values of 72 degrees

Closure Given sin 8 deg = , cos 8 deg = , and tan 8 deg = , find the 6 trig function values of 82 degrees HW: p.444 # odds

5.1 Review Tues Oct 21 Do Now Evaluate in exact value 1) csc 45 deg 2) cos 60 deg

HW Review: p.444 #17-101

Closure What are the 6 trig functions? What do they tell us? HW: none