Question

The graphs of \( f(x)=a \sin x \) and \( g(x)=\cos x+1 \) for \( x \in[0 ; 360] \) are sketched below. 6.1 Write down the value of \( a \). (1) 6.2 Write down the period of \( f \). (1) 6.3 Write down the range of \( g \). (2) 6.4 For which values of \( x \) for \( x \in\left[0^{\circ} ; 360^{\circ}\right] \) will \( f(x) . g(x)>0 \) ? (2) 6.5 The graph \( g \) is reflected about the \( x \)-axis and then shifted 2 units upwards to obtain the graph \( h \). Write down the equation of \( h \). (2) \( |8| \)

          The graphs of \( f(x)=a \sin x \) and \( g(x)=\cos x+1 \) for \( x \in[0 ; 360] \) are sketched below.
6.1 Write down the value of \( a \).
(1)
6.2 Write down the period of \( f \).
(1)
6.3 Write down the range of \( g \).
(2)
6.4 For which values of \( x \) for \( x \in\left[0^{\circ} ; 360^{\circ}\right] \) will \( f(x) . g(x)>0 \) ?
(2)
6.5 The graph \( g \) is reflected about the \( x \)-axis and then shifted 2 units upwards to obtain the graph \( h \). Write down the equation of \( h \).
(2)
\( |8| \)

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The graphs of f(x)=a sin x and g(x)=cos x+1 for x ∈[0 ; 360] are sketched below.
6.1 Write down the value of a.
(1)
6.2 Write down the period of f.
(1)
6.3 Write down the range of g.
(2)
6.4 For which values of x for x ∈[0^∘ ; 360^∘] will f(x) . g(x)>0 ?
(2)
6.5 The graph g is reflected about the x-axis and then shifted 2 units upwards to obtain the graph h. Write down the equation of h.
(2)
|8|

Added by Joel W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Mukesh Devi

Step 1

- The amplitude of \( f(x) = a \sin x \) is the absolute value of \( a \). - From the graph, the maximum value of \( f(x) \) is 1, so \( a = 1 \). Show more…

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The graphs of \( f(x)=a \sin x \) and \( g(x)=\cos x+1 \) for \( x \in[0 ; 360] \) are sketched below. 6.1 Write down the value of \( a \). (1) 6.2 Write down the period of \( f \). (1) 6.3 Write down the range of \( g \). (2) 6.4 For which values of \( x \) for \( x \in\left[0^{\circ} ; 360^{\circ}\right] \) will \( f(x) . g(x)>0 \) ? (2) 6.5 The graph \( g \) is reflected about the \( x \)-axis and then shifted 2 units upwards to obtain the graph \( h \). Write down the equation of \( h \). (2) \( |8| \)

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