Section 6.4 graphs of the sine, cosine, tangent, cotangent, cosecant, and secant functions
Warm-Up: Solve each equation. Students will define sine, cosine, and tangent ratios in right...
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Warm-Up: Solve each equation 1) 0.875= x 18 2) 24 y =0.5 3) y 25 = 0.96 4) 0.866x =12 5) 0.5x =18 1) 15. 2) 48 3) 24 4) 13 5) 36
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Trigonometric Ratios The relationships between the angles and the sides of a right triangle. Trignometric Ratios
Transcript of Warm-Up: Solve each equation. Students will define sine, cosine, and tangent ratios in right...
Warm-Up: Solve each equation
€
1) 0.875 =x
18
2) 24y
= 0.5
3) y
25= 0.96
4) 0.866x =12
5) 0.5x =18
€
1) 15.752) 483) 244) 13.95) 36
Students will define sine, cosine, and tangent ratios in right triangles.
Trigonometric RatiosThe relationships between the angles and the
sides of a right triangle.
Trignometric Ratios
How do I remember this?
Three basic ratios: • sine (sin), cosine (cos), tangent (tan)
Trigonometric Ratios TheoremLet ABC be a right triangle. The sine, the cosine, and the tangent of
the acute angle A are defined as follows:sin A =
cos A =
tan A =
A C
B
ac
b€
oppositehypotenuse
€
adjacenthypotenuse
€
oppositeadjacent
€
ac
€
bc
€
ab
It is known that a hill frequently use for sled riding has an angle of elevation of 300 at its bottom. If the length of a sledder’s ride is 52.6 feet estimate the height of the hill.
300
h52.6
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sin300 =h
52.6
€
52.6 • sin300 = h
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(52.6) • (0.5) = h26.3 = h
You want to find the height of a tower used to transmit cellular phone calls. You stand 100 feet away from the tower and measure the angle of elevation to be 400. How high is the tower?
400
100 ftyou
tower
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tan400 =t
100
€
100 • tan400 = t
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(100) • .8391 = t
€
84 ft ≈ t
Practice Time!
€
sinA =1215
= .8
€
cosA =9
15= .6
€
sinB =9
15= .6
€
cosB =1215
= .8
€
sin50 =x
15x ≈11.5
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cos63 =5x
x ≈11
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cos38 =x
21x ≈16.5
