Problem 1 :
For the measures in the figure shown below, compute sine, cosine and tangent ratios of the angle θ.
Solution :
In the given right angled triangle, note that for the given angle θ, PR is the ‘opposite’ side and PQ is the ‘adjacent’ side.
Then,
sin θ = opposite side / hypotenuse = PR/QR = 35/37
cos θ = adjacent side / hypotenuse = PQ/QR = 12/37
tan θ = opposite side / adjacent side = PR/PQ = 35/12
Problem 2 :
Find the six trigonometric ratios of the angle θ using the diagram shown below.
Solution :
In the given right angled triangle, note that for the given angle θ, AC is the ‘opposite’ side and AB is the ‘adjacent’ side.
And also, the length of the adjacent side 'AB' is not given.
Find the length of AB.
By Pythagorean Theorem,
BC2 = AB2 + AC2
252 = AB2 + 72
625 = AB2 + 49
Subtract 49 from each side.
576 = AB2
242 = AB2
24 = AB
Then,
sin θ = opposite side / hypotenuse = AC/ BC = 7/25
cos θ = adjacent side / hypotenuse = AB/BC = 24/25
tan θ = opposite side / adjacent side = AC/AB = 7/24
csc θ = 1 / sin θ = 25/7
sec θ = 1 / cos θ = 25/24
cot θ = 1 / tan θ = 24/7
Problem 3 :
If tan A = 2/3, then find all the other trigonometric ratios.
Solution :
tan A = opposite side / adjacent side = 2 / 3
By Pythagorean Theorem,
AC2 = AB2 + BC2
AC2 = 32 + 22
AC2 = 9 + 4
AC2 = 13
AC = √13
Then,
sin A = opposite side / hypotenuse = BC/ AC = 2/√13
cos A = adjacent side / hypotenuse = AB/AC = 3/√13
csc A = 1 / sin A = √13/2
sec A = 1 / cos A = √13/3
cot A = 1 / tan A = 3/2
Problem 4 :
If sec θ = 2/3, then find the value of
(2sin θ - 3cos θ) / (4sin θ - 9cos θ)
Solution :
sec θ = hypotenuse / adjacent side = 13 / 5
By Pythagorean Theorem,
BC2 = AB2 + AC2
132 = 52 + AC2
169 = 25 + AC2
Subtract 25 from each side.
144 = AC2
122 = AC2
12 = AC
Then,
sin θ = opposite side / hypotenuse = AC/BC = 12/13
cos θ = adjacent side / hypotenuse = AB/BC = 5/13
(2sin θ - 3cos θ) / (4sin θ - 9cos θ) :
= (2 ⋅ 12/13 - 3 ⋅ 5/13) / (4 ⋅ 12/13 - 9 ⋅ 5/13)
= (24/13 - 15/13) / (48/13 - 45/13)
= [(24 - 15)/13] / [(48 - 45)/13]
= (9/13) / (3/13)
= (9/13) ⋅ (13/3)
= 9/3
= 3
So,
(2sin θ - 3cos θ) / (4sin θ - 9cos θ) = 3
To learn SOHCAHTOA in detail,
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
©All rights reserved. onlinemath4all.com
May 23, 22 01:59 AM
Exponential vs Linear Growth Worksheet
May 23, 22 01:59 AM
Linear vs Exponential Growth - Concept - Examples
May 23, 22 01:34 AM
SAT Math Questions on Exponential vs Linear Growth