ABC is a right-angled triangle where ZABC = 90°. BC is produced to D and tan B C Write down each of the following as a fraction, without the use of a calculator. ) sin ZACB ) cos ZBAC cos ZACD =) D uestion 2 T ithout using a calculator, evaluate tan- 47 3 tan R3 COST 3 uestion 3 nd the exact value of each of the following, without using a calculator. O sin 225° O tan estion 4 me curve y = a sin bx + c, where a, b and c are positive integers, is defin € 120°

Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter5: Identities And Formulas
Section: Chapter Questions
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Question 5
The curve, y = a cos
Given that the amplitude of y is 5 and that the period of y is 720°.
(a) State the value of a and of b.
(b) Given that the minimum value of y is -7, state the value of c.
(c) Sketch the graph of y, indicating clearly the coordinates of any maximum or minimum points on
the graph.
(d) State the range of values of k for which the equation a cos
Question 6
Given that cos 0 =
(a) sin 0,
(b) tane.
+c is defined for 0° ≤x≤720°, where a, b and c are integers.
Question 9
Given that tan 0 =
Question 7
Given that cosec.x=2 and cosx<0, without using a calculator, find the exact value of
(a) cosx,
(b) cotx.
(a) cose.
(b) cosec.
5
and 180° << 360°, without using a calculator, find the value of
13
Question 8
Given that cos= a and that 0° <0<90°, express tan(-0) in terms of a.
+c=k has 2 unique solutions.
1
-, where 90° < 0 <180° and p is a positive real number, express in terms of p,
р
Question 10
Find obtuse angles A and B such that
(a) cos A=-0.785,
(b) sin B=0.866.
Correct your answers to 1 decimal place.
Question 11
Solve 2 cosx+5 sinx=0 for 0<x<2π.
Question 12
Find the angle y where 0° ≤ y ≤ 360° such that
3
1+ 4 tan y
2
Transcribed Image Text:Question 5 The curve, y = a cos Given that the amplitude of y is 5 and that the period of y is 720°. (a) State the value of a and of b. (b) Given that the minimum value of y is -7, state the value of c. (c) Sketch the graph of y, indicating clearly the coordinates of any maximum or minimum points on the graph. (d) State the range of values of k for which the equation a cos Question 6 Given that cos 0 = (a) sin 0, (b) tane. +c is defined for 0° ≤x≤720°, where a, b and c are integers. Question 9 Given that tan 0 = Question 7 Given that cosec.x=2 and cosx<0, without using a calculator, find the exact value of (a) cosx, (b) cotx. (a) cose. (b) cosec. 5 and 180° << 360°, without using a calculator, find the value of 13 Question 8 Given that cos= a and that 0° <0<90°, express tan(-0) in terms of a. +c=k has 2 unique solutions. 1 -, where 90° < 0 <180° and p is a positive real number, express in terms of p, р Question 10 Find obtuse angles A and B such that (a) cos A=-0.785, (b) sin B=0.866. Correct your answers to 1 decimal place. Question 11 Solve 2 cosx+5 sinx=0 for 0<x<2π. Question 12 Find the angle y where 0° ≤ y ≤ 360° such that 3 1+ 4 tan y 2
Question 1
AABC is a right-angled triangle where ZABC = 90°. BC is produced to D and tan ZACB = 4
3
B
D
C
Write down each of the following as a fraction, without the use of a calculator.
(a) sin ZACB
(b) cos ZBAC
(c) cos ZACD
Question 2
TC
T
Without using a calculator, evaluate tan tan
6 3
4π
3
TC
COS-
3
Question 3
Find the exact value of each of the following, without using a calculator.
(a) sin 225°
(b) tan
Question 4
The curve y = a sin bx + c, where a, b and c are positive integers, is defined for 0° ≤x≤180°, h=
amplitude of 3 and a period of 120°.
(a) State the value of a and of b.
(b) Given that the minimum value of y is 4,
(i) state the value of c.
(ii) sketch the graph of y.
Transcribed Image Text:Question 1 AABC is a right-angled triangle where ZABC = 90°. BC is produced to D and tan ZACB = 4 3 B D C Write down each of the following as a fraction, without the use of a calculator. (a) sin ZACB (b) cos ZBAC (c) cos ZACD Question 2 TC T Without using a calculator, evaluate tan tan 6 3 4π 3 TC COS- 3 Question 3 Find the exact value of each of the following, without using a calculator. (a) sin 225° (b) tan Question 4 The curve y = a sin bx + c, where a, b and c are positive integers, is defined for 0° ≤x≤180°, h= amplitude of 3 and a period of 120°. (a) State the value of a and of b. (b) Given that the minimum value of y is 4, (i) state the value of c. (ii) sketch the graph of y.
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