Trigonometric Identity Proving is a common question type that is included in the O-Level Additional Math syllabus. The mention of “trigo proving” would often cause even the top secondary school students to break out in cold sweat. Data recovery pro 1 1 keygen torrent.
Example 1 :
- Proving Trigonometric Identities (page 1 of 3) Proving an identity is very different in concept from solving an equation. Though you'll use many of the same techniques, they are not the same, and the differences are what can cause you problems.
- Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations.
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- Trig Prove each identity; 1. Secx - tanx SInX - secx 3. Sec8sin8 tan8+ cot8 sin' 8 5.cos ' Y -sin., y = 12' - Sin Y 7. Sec2 e sec2 e-1 csc2 e Identities worksheet 3.4 name: 2.
A ramp for unloading a moving truck, has an angle of elevation of 30°. If the top of the ramp is 0.9 m above the ground level, then find the length of the ramp.
Solution :
The side which is opposite to 90 degree is known as hypotenuse side, the side which is opposite to θ is known as opposite side and the remaining side is known as adjacent side.
In the given problem,we have to find the length of hypotenuse side and we know the length of opposite side.
AC = Hypotenuse side
AB = Opposite side
BC = Adjacent side
sin θ = opposite side/hypotenuse side
sin 30° = AB/AC
1/2 = 0.9/AC
AC = 0.9 x 2
Solving Trig Identities Examples
AC = 1.8 m
Therefore, the length of ramp is 1.8 m.
Example 2 :
A girl of height 150 cm stands in front of a lamp-post and casts a shadow of length 150 √3 cm on the ground. Find the angle of elevation of the top of the lamp-post.
Solution :
In the given problem,we have to find the angle inclined C.
AC = Hypotenuse side
AB = Opposite side = 150 cm
BC = Adjacent side = 150 √3 cm
tan θ = opposite side/Adjacent side
tan θ = AB/BC
tan θ = 150/150 √3
tan θ = 1/√3
θ = 30°
Example 3 :
Suppose two insects A and B can hear each other up to a range of 2 m. The insect A is on the ground 1 m away from a wall and sees her friend B on the wall, about to be eaten by a spider. If A sounds a warning to B and if the angle of elevation of B from A is 30°, will the spider have a meal or not ? ( Assume that B escapes if she hears A calling )
Solution :
In the given problem,we have to the length of AB.
AC = Hypotenuse side
BC = Opposite side = 1 m
AC = Adjacent side
sin θ = Opposite side/Hypotenuse side
sin θ = BC/AB
sin 30° = 1/AC
1/2 = 1/AC
AC = 2 m
So, the spider B escapes.
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